The legs of a right triangle are 8 cm and 12 cm. The hypotenuse of a similar triangle is 20 cm. What is the area, in cm?, of the larger triangle?

Thank you!

Given:

The legs of a right triangle are 8 cm and 12 cm.

The hypotenuse of a similar triangle is 20 cm.

To find:

The area of the larger triangle.

Solution:

According to the Pythagoras theorem,

The legs of a right triangle are 8 cm and 12 cm.

Taking square root on both sides.

The hypotenuse of a similar triangle is 20 cm. So, scale factor is

So, legs of larger triangle are

Area of triangle is

Therefore, the area of the larger triangle is about 92.31 sq cm.