Question

solve two rectangular fields, both measured in yards, are modeled below. what value of x, in rds, would cause the fields to have equal areas?

Explanation:

Step1: Find area of first rectangle

Length of first rectangle: \( x + 4 \), Width: \( 6 \). Area \( A_1 = 6(x + 4) \)

Step2: Find area of second rectangle

Length of second rectangle: \( x \), Width: \( 8 \). Area \( A_2 = 8x \)

Step3: Set areas equal and solve

\( 6(x + 4) = 8x \)
Expand: \( 6x + 24 = 8x \)
Subtract \( 6x \): \( 24 = 2x \)
Divide by 2: \( x = 12 \)

Answer:

\( x = 12 \)