Question
Find the value of p. Leave your answer in simplest radical form.
- 22
- 22√2
- 44
- 44√3
Hint:
We are given a right-angled triangle. It is 45°-45°-90° triangle. We are given the length of the hypotenuse. We are asked to find the value of one of its length. It is denoted by “p”. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 22√2
Let the given triangle be ABC
∠ABC = 90°
AB = p
AC = 44
It is a 45°-45°-90° triangle. The two angles of the triangle are same. It means the sides opposite to the triangle are equal. When a triangle has two sides equal, it is an isosceles triangle.
The given triangle is an isosceles triangle.
AB = BC
So, BC = p
Now, we will use the Pythagoras theorem. It states that, the square of the hypotenuse is equal to the sum of the square of the two sides.
AC2 = AB2 + BC2
44 = p2 + p2
1936 = 2p2
Rearranging we get,
2p = 1936
Dividing both the sides by 2 we get,
p2 = 2 × 484
Taking the square root we get
p = 22√2
Therefore, the value of p is 22√2.
For such questions, we should know the properties of different triangles.
Related Questions to study
The decreasing order of nucleophilicity among the nucleophiles :
A)
B)
C)
D)
The decreasing order of nucleophilicity among the nucleophiles :
A)
B)
C)
D)
Phenols are converted into their salts by aqueous NaOH but not by aqueous bicarbonates. The salts are converted into the free phenols by aqueous mineral acids, carboxylic acid or carbonic acids. Most phenols have Ka value of about 10–10, and are tremendously more acidic than alcohols. The difference in acidity are due to difference in stabilities of reactants and products. Phenol and phenoxide ions contain benzene ring and therefore must be hybrid of Kekuley structures
Being basic, oxygen can share more than a pair of electron with the ring
Since energy must be supplied to separate opposite charge, the structure of phenols should contain more energy. The net effect of resonance is therefore to stabilise the phenoxide ion to a greater extent than the phenol and thus to shift the equilibrium towards ionization and make Ka larger than for an alcohol.
Consider the following curves :
Phenols are converted into their salts by aqueous NaOH but not by aqueous bicarbonates. The salts are converted into the free phenols by aqueous mineral acids, carboxylic acid or carbonic acids. Most phenols have Ka value of about 10–10, and are tremendously more acidic than alcohols. The difference in acidity are due to difference in stabilities of reactants and products. Phenol and phenoxide ions contain benzene ring and therefore must be hybrid of Kekuley structures
Being basic, oxygen can share more than a pair of electron with the ring
Since energy must be supplied to separate opposite charge, the structure of phenols should contain more energy. The net effect of resonance is therefore to stabilise the phenoxide ion to a greater extent than the phenol and thus to shift the equilibrium towards ionization and make Ka larger than for an alcohol.
Consider the following curves :
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
What will be the products in following reactions
Symmetrically substituted epoxides give the same products in both the acid catalysed and base catalyzed ring opening. An unsymmetrical epoxide gives different products under acid catalysed and base catalysed conditions. Under basic conditions, the alkoxide ion simply attacks the less hindered carbon atom in an 2 displacement. Under acidic conditions, the alcohol, attacks the protonated epoxide
Structure II and III show that the oxirane carbon share part of positive charge. The tertiary carbon bear a larger part of positive charge and it is more strongly electrophilic. The bond between tertiary carbon and oxygen is weaker implying a lower transition state energy for attack at the tertiary carbon. Attack by the weak nucleophilic is sensitive to the strength of electrophilic is sensitive to the strength of electrophile. Centre attack takes place at more electrophilic carbon which is usually the more substituted carbon because it can better support the positive charge
What will be the products in following reactions
Alcohols undergo acid catalysed elimination reactions to produce alkenes. Because water is lost in the elimination, this reaction is called dehydration reaction. Secondary and tertiary alcohols always give E1 reaction in dehydration. Primary alcohols whose b-carbon is branched also give E1 reaction. The reactivity of alcohol for elimination reaction is tertiary alcohol > Secondary alcohol > Primary alcohol
Identify the product in the given reaction :
Alcohols undergo acid catalysed elimination reactions to produce alkenes. Because water is lost in the elimination, this reaction is called dehydration reaction. Secondary and tertiary alcohols always give E1 reaction in dehydration. Primary alcohols whose b-carbon is branched also give E1 reaction. The reactivity of alcohol for elimination reaction is tertiary alcohol > Secondary alcohol > Primary alcohol
Identify the product in the given reaction :
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Find the values of x and y.
If your answers are not integers, it should be in simplest radical form.
For such questions, we should know about the properties of a right-angled triangle and 30°-60°-90° triangle. The alternate way to solve the above question is by Pythagoras theorem and trigonometric ratios.
Find the values of x and y.
If your answers are not integers, it should be in simplest radical form.
For such questions, we should know about the properties of a right-angled triangle and 30°-60°-90° triangle. The alternate way to solve the above question is by Pythagoras theorem and trigonometric ratios.
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For such questions, we should know the properties of different triangles.
Find the length of the hypotenuse. leave your answer in simplest radical form.
For such questions, we should know the properties of different triangles.