Question

What is the length and the width of a rectangle with perimeter of 48 inches if its length is 7 inches longer than its width.

Answer 1

Width = 8.5 inches

Length = 15.5 inches

Explanation:

Width = W

Length = 7 + W

Perimeter = 2(Length) + 2(Width)

Substitute

48 = 2(7 + W) + 2(W)

Multiply

48 = 14 + 2W + 2W

Add

48 = 14 + 4W

Subtract 14 from both sides of the equation

34 = 4W

Divide both sides of the equation by 4

W = 8.5

Width = 8.5 inches

Length = 7 + Width = 7 + 8.5 = 15.5 inches

Hope this helps :)

Answer 2

Length and the width of the rectangle is 15.5 inches and 8.5 inches respectively.

Explanation:

Given:

Length = 7 inches + Width

=> P = 48 inches

=> L = (7 + W) inches............. (1)

Perimeter 'P' is the sum of all sides of the rectangle 2 (L + W)

∴ 48 inches = 2 (L + W) .................(2)

Substitute for L in equation (2)

∴ 48 inches = 2 [(7 + W) + W]

48 = 2[7 + 2W]

48 = 14 +4W

48 - 14 = 4W

34 = 4W

W = 8.5 inches

Recall that: Length, L = (7 + W)

∴ L = (7 + 8.5)

L = 15.5 inches