Question

The areas of two similar triangles are $45$ sq. cm and $80$ sq. cm. The sum of their perimeters is $35$ cm. Find the perimeter of each triangle in cm.

• A. $15,20$
• B. $13,22$
• C. $17,18$
• D. None of these

Answer 1

Answer: (A)

$15,20$

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

Let their perimeters be $x$ and $y$

$\Rightarrow \frac{45}{80}={\left(\frac{x}{y}\right)}^2{\left(\frac{x}{y}\right)}^2=\frac{9}{16}\frac{x}{y}=\frac{3}{4}4x=3y.....\left(i\right)$

Also given $x+y=\mathrm{35.....}\left(ii\right)$

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

$\Rightarrow x=15,y=20$

So option $A$ is correct.