Question

squares stuv and wxyz are similar. the ratio of the side lengths of square stuv to the side lengths of square wxyz is 5 : 7. what is the length of side wz? enter your answer in the box below. wz = \boxed{}

Explanation:

Step1: Identify side length of STUV

From the diagram, side length of square \( STUV \) (e.g., \( SV \)) is \( 15 \).

Step2: Set up proportion for similar squares

Let side length of \( WXYZ \) ( \( WZ \)) be \( x \). The ratio of sides \( STUV:WXYZ = 5:7 \), so \( \frac{15}{x}=\frac{5}{7} \).

Step3: Solve for \( x \)

Cross - multiply: \( 5x = 15\times7 \). Then \( 5x = 105 \), divide both sides by \( 5 \): \( x=\frac{105}{5}=21 \).

Answer:

\( 21 \)