Question

In the following figure $\Delta ABC\sim \Delta APQ,A\left(\Delta APQ\right)=4A\left(\Delta ABC\right)$. Find the ratio $\frac{BC}{PQ}$

• A. $1:1$
• B. $1:2$
• C. $1:3$
• D. $1:4$

Answer 1

Answer: (B)

$1:2$

$\Delta ABC\sim \Delta APQ$ (Given)

Apply the properties of similar triangles

$\therefore \frac{A\left(\Delta ABC\right)}{A\left(\Delta APQ\right)}=\frac{B{C}^2}{P{Q}^2}$ ......$\left(i\right)$

[$\therefore$ Ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides]

But $A\left(\Delta APQ\right)=4A\left(\Delta ABC\right)$ (given)

$\therefore \frac{A\left(\Delta ABC\right)}{A\left(\Delta APQ\right)}=\frac{1}{4}$ [From $\left(i\right)$ and $\left(ii\right)$
$\therefore \frac{BC}{PQ}=\frac{1}{2}$