Question
If LM=14 and MN=11, KM=?
- 16
- 18.76
- 17.82
- 15.12
Hint:
We are given a right-angled triangle KLM. An altitude is drawn from the vertex having the right angle. It divides the base of the triangle into two parts. The values of parts are given. We are asked to find the value of the KM. To solve this question, we will use the properties of a right-angled triangle.
The correct answer is: 17.82
The point where altitude meets is “N”
From the figure, we can write the values of lengths and angles.
Length of LM = 14
Length of MN = 11
Angle KLM = 90°
Let the value of altitude be “a”.
If we see, LM is a hypotenuse of the ∆LNM
We will use Pythagoras theorem. Pythagoras theorem states that, the square of the hypotenuse is equal to sum of the square of the other sides.
LM2 = LN2 + NM2
142 = a2 + 112
196 = a2 + 121
a2 = 196 – 121
a2 = 75
Taking square roots
a = 8.66
Therefore, the length of the LN is 8.66
Due to the altitude, two right-angled triangles are formed.
There is a theorem for altitude drawn from the right angle of a right-angled triangle. It states that, “When altitude is drawn from a right angle, two similar triangles are formed. They are similar to each other. They are also similar to the parent triangle”.
Triangle KNL~ LNM
So, the ratio of their sides will be equal.
Let the value of KN be “b”
We will find KM now.
KM = KN + NM
= 6.81 + 11
KM = 17.81
To solve such questions, we should know the properties of right-angled triangles and similar triangles. To find the altitude, we can just remember that the square of the altitude is equal to product of the two values
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