Question

rectangles w and x are similar. if the area of rectangle w is 128, what is the area of rectangle x? rectangle w area = 128 rectangle x

Explanation:

Step1: Find the ratio of side lengths

The ratio of the side lengths of rectangle \(X\) to rectangle \(W\) is \(\frac{8}{16}=\frac{1}{2}\)

Step2: Use the ratio - area relationship for similar figures

For similar figures, if the ratio of side lengths is \(k\), the ratio of areas is \(k^{2}\). Here \(k = \frac{1}{2}\), so the ratio of the area of \(X\) to the area of \(W\) is \((\frac{1}{2})^{2}=\frac{1}{4}\)

Let the area of rectangle \(X\) be \(A\). We know that \(\frac{A}{128}=\frac{1}{4}\)

Step3: Solve for the area of rectangle \(X\)

Cross - multiply: \(A=\frac{128\times1}{4}\)

\(A = 32\)

Answer:

The area of rectangle \(X\) is \(32\)