Question

The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.

Enter a number answer only.

Answer 1

Width = 10 inches

Explanation:

Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.

We can establish the following values to help us solve for the width of a rectangle:

Perimeter (P) = 68 inches

Length (L) = 14 + W inches

Width (W) = unknown

Solve for the Width (W)

P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.

Divide both sides by 2:

`\displaystyle\mathsf{(P)/(2)\:=\:(2(L\:+\:W))/(2)}`

`\displaystyle\mathsf{(P)/(2)\:=L\:+\:W}`

Substitute the value of the Perimeter and the length (L) into the formula:

`\displaystyle\mathsf{(68)/(2)\:=14\:+W\:+\:W}`

Combine like terms on the right-hand side, and simplify the left-hand side of the equation:

`\displaystyle\mathsf{34\:=14\:+2W}`

Subtract 14 from both sides:

34 - 14 = 14 - 14 + 2W

20 = 2W

Divide both sides by 2 to solve for the width (W):

`\displaystyle\mathsf{(20)/(2)\:=\:(2W)/(2)}`

W = 10 inches

Therefore, the width of the rectangle is 10 inches.

Double-check:

Verify whether the derived value for the width is correct:

P = 2L + 2W

68 = 2(14 + 10) + 2(10)

68 = 2(34) + 20

68 = 48 + 20

68 = 68 (True statement).

Thus, the length of the rectangle is 34 inches, and the width is 10 inches.