The length of a rectangle is 4 m longer than it’s width. If the perimeter of the rectangle is 36 m, find it’s area.

Answer 1

We can translate "the length of a rectangle is 4 m longer than its width" into an algebraic expression:

L = W + 4

Perimeter of a rectangle is 2L + 2W:

P = 2L + 2W

Substituting in (W + 4) for L:

P = 2(W + 4) + 2W

P = 4W + 8

Since we know perimeter is 36 m, set the perimeter expression equal to 36 and solve for W:

4W + 8 = 36

W = 7

We know how to find L from the expression above:

L = W + 4 = (7) + 4 = 11

Area of a rectangle is LW, so:

A = LW = (11)(7) = 77 m²

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