Exercise 35 Page 640

Notice that the given triangles are both right triangles with a pair of congruent acute angles. Therefore, by the Angle-Angle Similarity Theorem, they are similar right triangles.

We are told that the area of the smaller triangle is $6{\text{ cm}}^2.$ If we calculate the area of the larger triangle, we will be able to find the area scale factor and therefore the scale factor. This will allow us to find $x$ and $y.$ To find the area of the larger triangle, we must recall that the area of a triangle is half the product of its base and its height.