First, re-read the problem until you understand it and can put it into your own words. I re-wrote it like this: "Find the area of a rectangle by first finding the length (L) and the width (W)." [note that I added "find L and W," but that is how I'm going to solve the problem; I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).

Translate the problem:

"The length of a rectangle is 3 ft longer than its width" means

L = 3 + W (eq1)

"the perimeter of the rectangle is 30 ft" means

P = 30 (eq2)

So, now the math is easy, just find L and W so we can compute the area:

P = 30 = 2L + 2W (eq3; from eq2 and the formula for P)

30 = 2(3+W) + 2W (use eq1 to substitute for L)

30 = 6 + 2W + 2W (distribute)

30 = 6 + 4W (collect terms)

24 = 4W (subtract 6 from both sides)

6 ft = W (divide both sides by 4)

Use the easiest equation (either eq1 or else eq3) to find L:

L = 3 + W (eq1)

L = 3 + 6

L = 9 ft

What is the area (A)?

A = L*W

A = (9 ft)*(6 ft)

A = 54 sq ft

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2 years ago