The length of a rectangle is two more than triple the width. If the perimeter is 92 inches, find the dimensions. The width is inches. The length is inches.

Answer 1

The perimeter of a rectangle is 2L + 2W.

The given conditions are that L = 3W + 2, and that 2L + 2W = 92.

replace L by 3W + 2, and write: 2(3W + 2) + 2W = 92.

Next, simplify the left side: 6W + 4 + 2W = 92 ⇒ 8W = 92 - 4 = 88 ⇒ W = 11 in.

Substituting this value of W gives L = 3(11) + 2 = 35 in.

For mental comfort, 2(35) + 2(11) = 70 + 22 = 92 in.

Answer 2

Perimeter of a rectangle is P = 2L + 2W

Here the P is 92 inches, Triple the width is 3W

The length is two more than triple the width, so L = 3W + 2

Then 92 = 2(3W + 2) + 2W by substitution. Use distributive rule to eliminate the parentheses.

92 = 6W + 4 + 2W. Combine like terms, etc.

88 = 8W, so W = 88/8 = 11 inches.

L = 3(11) + 2 = 35 inches.

Check: Perimeter = 11 + 11+ 35+ 35 = 92