SOLUTION: the length of a diagonal of this rectangle is 34 m. given that the shorter sides are 14 m shorter than the longer sides, find the area

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Question 720750: the length of a diagonal of this rectangle is 34 m. given that the shorter sides are 14 m shorter than the longer sides, find the area
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the length of the rectangle. Since the width is 14 less, it would be x - 14.

The length, width and diagonal of the rectangle form a right triangle. (Draw a diagram if this doesn't make sense.) So they must fit the Pythagorean Theorem:
x%5E2+%2B+%28x-14%29%5E2+=+34%5E2
x%5E2+%2B+x%5E2-28x%2B196+=+1156
2x%5E2-28x%2B196=1156
2x%5E2-28x-960=0
2%28x%5E2-14x-480%29=0
2%28x-30%29%28x%2B16%29=0
x-30 = 0 or x+16 = 0
x = 30 or x = -16

Since x is the length of a rectangle and since negative lengths make no sense, we will reject the second solution. So x = 30.

To find the area of the rectangle we need both the length and width. The width is x-14 . Since x = 30, the width is 30-14 = 16. Now we can find the area:
A = l*w = 30*16 = 480