Question

The area of two similar triangles are $16c{m}^2$ and $36c{m}^2$ respectively, If the altitudes are in the ratio $2:x$, then the value of $x$ is

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is B $3$

REF.Image

Consider two trianles ABC and PQR with AM and PN as altitudes respectively.

$\frac{areaof\Delta ABC}{areaof\Delta PQR}=\frac{16}{36}$

We know $\frac{areaof{\Delta }_1}{areaof{\Delta }_2}$ = square of radius of proportional sides.

so $\frac{BC}{QR}=\frac{16}{36}=\frac{4}{9}$ _______ (1)

$\frac{Areaof\Delta ABC}{Areaof\Delta PQR}=\frac{\frac{1}{2}BC\times AM}{\frac{1}{2}QR\times PN}=\frac{16}{36}=\frac{4}{9}$

$\Rightarrow \frac{BC}{QR}\times \frac{AM}{PN}=\frac{4}{9}$

Given $\frac{BC}{QR}=\frac{2}{3}\Rightarrow \frac{2}{3}\times \frac{AM}{PN}=\frac{4}{9}$

$\Rightarrow \frac{AM}{PN}=\frac{2}{3}$

$\therefore x=3$