Question

The triangles are similar. The area of the larger triangle is 1360 cm².

What is the area of the smaller triangle?

Smaller triangle is labeled 16 cm.
Larger triangle is labeled 64 cm

(they are both scalene triangles)

Answer 1

The answer is 85^2

Explanation:

Answer 2

If two triangles are similar, the correspondant angles are in the same proportion.

This means that, in order to obtain a certain side of the smaller triangle, you have to divide the larger side by a fixed ratio.

We're given the example of two correspondant angles, labeled 64 and 16. Since 16 is one-fourth of 64, the scale factor is 1/4.

The areas of the two triangles are not exactly in this ratio, instead they follow the square of this ratio.

So, if the smaller sides are 1/4 of the larger sides, the smaller area is 1/16 of the larger area.

So, the smaller area is

`(1360)/(16) = 85`