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 + 2(w + 5) = 60 )

b. ( 2w + 2(w - 5) = 60 )

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

d. ( 2(w - 5) + 2w = 60 )

Explanation:

Step1: Define variables

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

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 \( P = 60 \), so the equation is \( 2(w + 5) + 2w = 60 \), which is equivalent to \( 2w + 2(w + 5)=60 \) (by commutative property of addition in addition of terms).

Answer:

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