Question

A rectangles length is 8 feet longer than twice its width. The rectangles perimeter is 316 feet. Find the rectangles length and width.

The rectangles length is ______ feet, and its width is_____feet.

Answer 1

length= 108 feet,

width= 50 feet

Overview of steps:

1. Define variables
2. Form two equations using given information
3. Solve for one variable through substitution/ elimination
4. Solve for the other variable through substitution

Working:

Let the length and the width of the rectangle be L and W feet respectively.

L= 2W +8 -----(1)

Perimeter= 2(length) +2(width)

316= 2L +2W

2L +2W= 316

Divide both sides by 2:

L +W= 158 -----(2)

Substitute (1) into (2):

2W +8 +W= 158

Simplify:

3W +8= 158

3W= 158 -8

3W= 150

Divide both sides by 3:

W= 150 ÷3

W= 50

Substitute W= 50 into (1):

L= 2(50) +8

L= 100 +8

L= 108

Thus, the rectangle's length is 108 feet, and its width is 50 feet.