Question

a store sells rectangular picture frames. • frame a has a width of 8 inches and a length of 10 inches. • frame b has a width that is 4 inches greater than the width of frame a. • frame a and frame b are similar rectangles. what is the length, in inches, of frame b?

Explanation:

Step1: Find width of Frame B

Frame A width = 8 in, Frame B width = 8 + 4 = 12 in.

Step2: Set up proportion for similar rectangles

Let \( l_B \) be length of Frame B. Since similar, \( \frac{\text{Width}_A}{\text{Length}_A} = \frac{\text{Width}_B}{\text{Length}_B} \), so \( \frac{8}{10} = \frac{12}{l_B} \).

Step3: Solve for \( l_B \)

Cross - multiply: \( 8l_B = 10\times12 \), \( 8l_B = 120 \), \( l_B=\frac{120}{8}=15 \).

Answer:

15