SOLUTION: If the length of a rectangle is 3 feet longer than the width and the diagonal is 15 feet, then what are the length and the width?

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Question 186849: If the length of a rectangle is 3 feet longer than the width and the diagonal is 15 feet, then what are the length and the width?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let width be w. Then Length is (w+3)
a%5E2+%2B+b%5E2+=+c%5E2 pythagorean theorem
w%5E2+%2B+%28w%2B3%29%5E2+=+15%5E2
w%5E2+%2B+w%5E2+%2B+6w+%2B+9+=+225
2w%5E2+%2B+6w+-+216+=+0
2%28w-9%29%28w%2B12%29+=+0
w = 9 or w = -12. Since a width cannot be negative, then w = 9. And length = 12
Notice the triangle formed by width:length:diagonal is in the ration 3:4:5 -- a common ratio for right triangles and one you would do well to 'recognize on sight'.