Question

Rectangle ABCD is similar to Rectangle WXYZ . The area of ABCD is 30 square inches. Explain how to find the area, x , of WXYZ. AD/WZ = 1/2 AB/WX = 1/2 Because the ratio of the corresponding side lengths is 1/2, the ratio of the areas is equal to (__/__) to the second power. To find the area, solve the proportion 30/x = __/__ to get x = ___.

Answer 1

120 square inches

Explanation:

From the above question, we are told that:

Rectangle ABCD is similar to Rectangle WXYZ .

The area of ABCD is 30 square inches.

We are also given the ratio of their side length = 1/2

To the find the area of the second rectangle, the scale factor = k² is required where:

k = ratio of the side lengths

Let us represent the area of the.secind Rectangle as = x

Because the ratio of the corresponding side lengths is 1/2, the ratio of the areas is equal to (1/2 ) to the second power.

Hence

30/x = k²

30/x = (1/2)²

30/x = 1/4

We cross Multiply

= 30 × 4 = x

x = 120 square inches.

Therefore, the area of Rectangle WXYZ is 120 square inches.