Question

1. the perimeter of a rectangular garden is 60 feet. if the length of the garden is 5 feet longer than its width, which equation represents this situation?

a. $2w + 2w + 5 = 60$
b. $2w + 2(w - 5) = 60$
c. $2w + 2(w + 5) = 60$
d. $2(w - 5) + 2w = 60$

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) feet. The length is 5 feet longer than the width, so length \( l = w + 5 \).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2l + 2w \).

Step3: Substitute length into formula

Substitute \( l = w + 5 \) into the perimeter formula: \( P = 2(w + 5) + 2w \). We know the perimeter is 60, so \( 2w + 2(w + 5)=60 \) (rearranged order of terms, but multiplication is commutative).

Answer:

c. \( 2w + 2(w + 5) = 60 \)