Question
A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. Find x?
- x = 19 cm
- x = 24 cm
- x = 3 cm
- x = 16.5 cm
Hint:
We are given the lengths of two triangles. They are similar triangles. For one triangle we are given all three sides. For the second triangle we are only given two sides. We are asked to find the value of the third side. To solve this question, we will use the properties of the similar triangles.
The correct answer is: x = 16.5 cm
Let the first triangle be ABC and second triangle be PQR.
The length of the sides are as follows:
For ∆ABC
AB = 11 cm
BC = 16 cm
AC = 16 cm
For ∆PQR
PQ = x cm
QR = 24 cm
PR = 24 cm
We are given that the triangles are similar. Similar triangles have same shape but their sizes are different.
The ratio of the sides of the similar triangles is equal. So, to find the side we will take the ratio of the sides.
Let’s take the ratio of the sides of the above triangles. .
. 
Let's solve for x. We will just take two ratios.
... 
x = 16.5 cm
Therefore, the value of x = 16.5 cm.
,
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio.
Related Questions to study
Two objects that are the same shape but not the same size are _______.
The objects which are identical are called as congruent objects.
Two objects that are the same shape but not the same size are _______.
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A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. Find the building tall.
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To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
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To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
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For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
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A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
