Answer:
Width = 6ft Area = 54 sq ft
Step-by-step explanation:
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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