SOLUTION: The length of a rectangle exceeds the width by 2cm. If the diagonal is 10cm long, find the width of the rectangle.

Question 529799: The length of a rectangle exceeds the width by 2cm. If the diagonal is 10cm long, find the width of the rectangle.
Found 2 solutions by jim_thompson5910, swincher4391:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
L^2 + W^2 = D^2

(W+2)^2 + W^2 = 10^2

W^2 + 4W + 4 + W^2 = 100

W^2 + 4W + 4 + W^2 - 100 = 0

2W^2 + 4W - 96 = 0

2(W^2 + 2W - 48) = 0

2(W + 8)(W - 6) = 0

W + 8 = 0 or W - 6 = 0

W = -8 or W = 6

Throw out the negative solution to get W = 6

So the width is 6 cm and the length is 6+2 = 8 cm

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Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let l and w be the length and width respectively. Let d be the diagonal.
l = w+2
Then look at this diagram:

Notice we have a right triangle.
Then w^2 + (w+2)^2 = (10)^2
w^2 + w^2 + 4w + 4 = 100
2w^2 + 4w -96 = 0
2(w^2 + 2w - 48) = 0
2(w+8)(w-6) = 0
w = -8 and w = 6
Can't have a negative width, so w=6.
Thus our width is 6cm.
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