Question

two rectangles have equal area, in square feet. • rectangle x has a width of 6 inches and a length of (2w − 8) inches. • rectangle y has a width of ½ inch and a length of (32 − 8w) inches. what is the value of w?

Explanation:

Step1: Calculate area of Rectangle X

Area of Rectangle X = width × length = \( 6 \times (2w - 8) \)

Step2: Calculate area of Rectangle Y

Area of Rectangle Y = width × length = \( \frac{1}{2} \times (32 - 8w) \)

Step3: Set areas equal (since areas are equal)

\( 6(2w - 8) = \frac{1}{2}(32 - 8w) \)
Multiply both sides by 2 to eliminate fraction: \( 12(2w - 8) = 32 - 8w \)
Expand left side: \( 24w - 96 = 32 - 8w \)
Add \( 8w \) to both sides: \( 32w - 96 = 32 \)
Add 96 to both sides: \( 32w = 128 \)
Divide by 32: \( w = 4 \)

Answer:

\( w = 4 \)