Question

8 the length of a rectangle is twice its width. if the perimeter, or distance around all four sides, of the rectangle measures 42 inches, what are the dimensions of the rectangle? use w to represent the width. a. length = 6 inches, width = 7 inches b. length = 14 inches, width = 3 inches c. length = 14 inches, width = 7 inches d. length = 42 inches, width = 21 inches

Explanation:

Step1: Define variables and formula

Let width be \( w \), length \( l = 2w \). Perimeter of rectangle: \( P = 2(l + w) \). Given \( P = 42 \), so \( 2(2w + w)=42 \).

Step2: Simplify and solve for \( w \)

Simplify: \( 2(3w)=42 \) → \( 6w = 42 \). Divide by 6: \( w=\frac{42}{6}=7 \).

Step3: Find length

Length \( l = 2w = 2\times7 = 14 \).

Answer:

C. length = 14 inches, width = 7 inches