Question

The perimeters of two similar triangles is in the ratio $3:4$. The sum of their areas is $75$ sq. cm. Find the area of each triangle in sq. cm.

• A. $30,45$
• B. $27,48$
• C. $25,50$
• D. None of these

Answer 1

The correct option is B $27,48$

If triangles are similar then the ratio of their areas is equal to square of their perimeters.

Let the areas be $x$ and $y$

$\Rightarrow \frac{x}{y}={\left(\frac{3}{4}\right)}^2\frac{x}{y}=\frac{9}{16}16x=9y.....\left(i\right)$

Also given $x+y=\mathrm{75.....}\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$

$\Rightarrow x=27,y=48$

So option $B$ is correct.