Question

$\Delta ABC\sim \Delta PQR$ and areas of two similar triangles are $64$sq.cm and $121$sq.cm respectively. If $QR=15$cm, then find the value of side BC.

• A. $\frac{120}{11}$
• B. $\frac{118}{11}$
• C. $\frac{115}{11}$
• D. $\frac{111}{11}$

Answer 1

The correct option is A $\frac{120}{11}$

$△ABC\sim △PQR$ ...Given

By theorem on ratio of similar triangles,

$\frac{Area\left(\Delta ABC\right)}{Area\left(\Delta PQR\right)}=\frac{B{C}^2}{Q{R}^2}$

$\Rightarrow \frac{64}{121}=\frac{B{C}^2}{(15{)}^2}$

$\Rightarrow \frac{8}{11}=\frac{BC}{15}$

$\Rightarrow BC=\frac{120}{11}$cm.