SOLUTION: The width of a rectangle is 2 ft less than the length. The area is 24ft^2. Find the length and the width

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Question 630577: The width of a rectangle is 2 ft less than the length. The area is 24ft^2. Find the length and the width
Answer by Taino(8) About Me  (Show Source):
You can put this solution on YOUR website!
Data:
W = L - 2
Area = 24 Ft^2

Equations:
a. Area of a rectangle = W * L

b. Quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

a. Area = W * L = (L-2) * L = 24 ----> L^2 - 2L - 24 = 0

b. Quadratic equation: a = 1, b = -2, c = -24



L = 1 +- 5 ----> L = 6 or L = -4, Since this is a rectangle being constructed the measurement cannot be negative and so the only logical answer can be L = 6.

If we now substitute 6 into the width equation which was given we get W=4.

Now we can verify that the area is indeed 24 ft^2 = 6*4.