SOLUTION: A rectangle is three times longer than it is wide and has a diagonal of 50. Find the dimensions of the rectangle and its perimeter.

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Question 381821: A rectangle is three times longer than it is wide and has a diagonal of 50. Find the dimensions of the rectangle and its perimeter.
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
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A rectangle is three times longer than it is wide and has a diagonal of 50. Find the dimensions of the rectangle and its perimeter.
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L = 4W
50%5E2+=+L%5E2+%2B+W%5E2+=+%284W%29%5E2+%2B+W%5E2
17W%5E2+=+2500
W+=+sqrt%282500%2F17%29
W =~ 12.12678 square units
L =~ 48.507 sq units
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Perimeter = 2L + 2W = 121.2678 units

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length and width be 3x and x, respectively. Since the diagonal is 50, we have
%283x%29%5E2+%2B+x%5E2+=+50%5E2+=+2500
10x%5E2+=+2500
x%5E2+=+250
x+=+5sqrt%2810%29 +3x+=+15sqrt%2810%29
Therefore the perimeter is 40sqrt%2810%29.