Question

Q. If ∆ABC ~ ∆APQ and ar(∆APQ) = 4ar(∆ABC), then ratio of BC to PQ is?
Ch - Triangles
Class 10th ​

Answer 1

Given,

$\[\begin{array}{l}\Delta ABC \cong \Delta APQ\\Ar.\left( {\Delta APQ} \right) = 4 \times Ar.\left( {\Delta ABC} \right)\end{array}\]$

To find,

The ratio of $\[\frac{{BC}}{{PQ}}.\]$

Solution,

Know that when two triangles are similar then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{BC}}{{PQ}} = \sqrt {\frac{{Ar.\left( {\Delta ABC} \right)}}{{Ar.\left( {\Delta APQ} \right)}}} \\ \Rightarrow \frac{{BC}}{{PQ}} = \sqrt {\frac{{Ar.\left( {\Delta ABC} \right)}}{{4 \times Ar.\left( {\Delta ABC} \right)}}} \\ \Rightarrow \frac{{BC}}{{PQ}} = \sqrt {\frac{1}{4}} \\ \Rightarrow \frac{{BC}}{{PQ}} = \frac{1}{2}\end{array}\]$

Hence, the ratio of $\[\frac{{BC}}{{PQ}}\]$ is$\[\frac{1}{2}.\]$