A rectangle has a length that is unknown but is 12 inches longer than its width, w. The perimeter of the rectangle is 104 inches.

Question

(a) Write an expression for the length of the rectangle in terms of w. Label it on the diagram. (b) Write an equation using the perimeter to find the value of w. Solve it for w.

Answer 1

a) Length, l = w+12

w

+---------------+

| |

| |

| |

| | l = w+12

| |

| |

+---------------+

perimeter p = 2w + 2l = 104

2w + 2(w+12) = 104

4w + 24 = 104

4w = 80

w = 80/4 = 20

Checking:

l = w + 12 = 32

2(20) + 2(32) = 40 + 64 = 104