SOLUTION: Hello, I am having a problem with the question "the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle. I keep getting

Question 481406: Hello,
I am having a problem with the question "the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle. I keep getting different answers.
Thanks in advance!
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the length of a rectangle exceeds the width by 2 cm. If the diagonal is 10 cm long, find the width of the rectangle.
.
Let w = width
then
w+2 = length
.
applying Pythagorean theorem we have:
w^2 + (w+2)^2 = 10^2
w^2 + (w+2)(w+2) = 100
w^2 + (w^2+4w+4) = 100
2w^2+4w+4 = 100
w^2+2w+2 = 50
w^2+2w-48 = 0
(w+8)(w-6) = 0
w = {-8, 6}
throw out the negative solution leaving:
w = 6 cm
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