SOLUTION: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 57 cm, what is the length of the diagonal?

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Question 403547: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 57 cm, what is the length of the diagonal?

Found 2 solutions by Nada, MathLover1:
Answer by Nada(11) About Me  (Show Source):
You can put this solution on YOUR website!
Area = Width x Length
57 = W x L
W= 2L-4
57 = 2L-4 x L
57 = 2L-4L
57 = 2L
L = 57/2 = 28.5
To get W :
57 = W x 28.5
W = 57/28.5 = 2
To check answer : 28.5 x 2 = 57 ( answer is correct)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The width, W,
The length L

W+%2B+4+=+2L...=>...L+=%28W+%2B+4%29%2F2

If the area of the rectangle is A+=57+cm,

what is the length of the diagonal d

A+=W%2AL
57cm+=+W%2A%28%28W+%2B+4%29%2F2%29

2%2A57cm+=+W%5E2+%2B+4W

114cm+=+W%5E2+%2B+4W

++W%5E2+%2B+4W+-+114+=+0

W+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-114%29+%29%29%2F%282%2A1%29+

W+=+%28-4+%2B-+sqrt%2816+%2B+456+%29%29%2F2+

W+=+%28-4+%2B-+sqrt%28472+%29%29%2F2+

W+=+%28-4+%2B-+%2821.73%29%29%2F2+

W+=+%28-4+%2B%2821.73%29%29%2F2+

W+=+17.73%2F2+

W+=+8.86....we don't need other root, width cannot be negative

L+=%28W+%2B+4%29%2F2

L+=%288.86+%2B+4%29%2F2

L+=%2812.86%29%2F2

L+=6.43

d%5E2+=+W%5E2+%2B+L%5E2

d%5E2+=+%288.86%29%5E2+%2B+%286.43%29%5E2

d%5E2+=+%2878.4996%29+%2B+%2841.3449%29

d%5E2+=+%28119.8445%29+

d%5E2+=+sqrt%28119.8445%29+

d+=+10.95........the length of the diagonal