Question
If KM=22 and MN=16, Find LM.
- 16
- 18.76
- 2.4
- 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 LM. To solve this question, we will use the properties of a right-angled triangle.
The correct answer is: 18.76
Let the point where altitude meets be “N”
From the figure, we can write the values of lengths and angles.
Length of KM = 22
Length of MN = 16
Angle KLM = 90°
KN = KM – MN
= 22 – 16
KN = 6
Let the value of altitude be “a”.
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.
If we see, LM is a hypotenuse of the ∆LNM
We will use Pythagoras to solve it further. Pythagoras theorem states that, the square of the hypotenuse is equal to sum of the square of the other sides.
LM2 = LN2+ NM2
LM2 = 9.792 + 162
= 96 + 256
= 352
Taking square roots
LM = 18.76
Therefore, the length of the LM is 18.76.
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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