Similar Triangles: Calculate Second Triangle Perimeter Given Areas 361cm² and 81cm²

In similar triangles, the area of the triangles is 361 cm² and 81 cm². If it is known that the perimeter of the first triangle is 38, what is the perimeter of the second triangle?

To begin with we can determine the perimeter of the second triangle by using the equation below.

$\frac{P_2}{P_1}=\sqrt{\frac{S_2}{S_1}}$

We insert the existing data

$\frac{P_2}{38}=\sqrt{\frac{81}{361}}$

$\frac{P_2}{38}=\frac{\sqrt{81}}{\sqrt{361}}=\frac{9}{19}$

Lastly we multiply by 38 to obtain the following answer:

$P_2=\frac{9}{19}\times38=18$