Question

In the figure, if QR-24m, NR 4m and MN 6m, then the length of PQ is

Answer 1

Given:

if QR =24 m, NR = 4 m and MN = 6 m. then find the length of PQ.

To find:

The length of PQ.​

Solution:

In Δ RNM and Δ RQP, we get

∠MRN = ∠PRQ . . . [common angle]

∠RNM = ∠RQP = 90° . . . [from the figure]

∴ Δ RNM ~  Δ RQP . . . [by AA similarity]

We know that →

The corresponding sides of the similar triangles are proportional to each other.

So, based on the above theorem, for the two similar triangles ΔRNM and Δ RQP, we get

$\frac{NR}{QR} = \frac{MN}{PQ}$

on substituting the given values of QR =24 m, NR = 4 m and MN = 6 m, we get

$\implies \frac{4}{24} = \frac{6}{PQ}$

$\implies \frac{1}{6} = \frac{6}{PQ}$

$\implies PQ = 6 \times 6$

$\implies \bold{PQ = 36 \:m}$

Thus, the length of PQ is → 36 m.

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