The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width.

Answer 1

This rectangle's width will be represented as w and the length as l. If the length is 3 more than twice the width, then algebraically it is l = 2w + 3.

The perimeter of the rectangle is the sum of each side: width plus width plus length plus length

w + w + l + l = 2w + 2l

If we know that the length is represented by l = 2w + 3 then we can substitute that in for into the equation for perimeter. After substitution, the equation for perimeter would be:

2w + 2(2w + 3) = 128

Distribute: 2w + 4w + 6 = 128

Combine like terms: 6w + 6 = 128

Subtract: 6w = 122

Divide: w = 20 1/3 feet

Substitute 20 1/3 in for w in the equation for length:

L = 2w + 3

L = 2(20 1/3) + 3

L = 40 2/3 + 3

L = 43 2/3 feet