Answer to Question #158229 in Geometry for Janine

Question

The area of a triangle is 72, and one side is 24. If the corresponding side

in a similar triangle is 16, find its area.

Answer 1

Let $A$ be area of the second triangle.

Since these triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

So, we have $\frac{A}{72}=\left( \frac{16}{24}\right)^2$

$A=72\cdot \left( \frac{16}{24}\right)^2=32$

Answer: area of the second triangle is $32$ .