SOLUTION: Rectangular state: One side of a rectangular stage is 2 meters longer than the other. If the diagnonal is 10 meters, then what are the lenths of the sides?

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Question 124363: Rectangular state: One side of a rectangular stage is 2 meters longer than the other. If the diagnonal is 10 meters, then what are the lenths of the sides?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of the stage(10m) represents the hypotenuse of a right triangle whose legs are the width (W) and the length (L) of the rectangle.
But the problem states that the length (L) is 2 meters longer than the width (W), so the length can be expressed as:
L = W+2.
Now we can apply the Pythagorean theorem (c%5E2=a%5E2%2Bb%5E2) to solve this problem since we are dealing with a right triangle.
c is the hypotenuse of the right triangle, or the diagonal of the rectangular stage which is given as 10m.
a and b are the width of the stage (W) and the length of the stage (L = W+2).
Make the appropriate substitutions into the Pythagorean formula to get:
10%5E2+=+L%5E2%2BW%5E2 Substitute L = W+2
100+=+%28W%2B2%29%5E2%2BW%5E2
100+=++%28W%5E2%2B4W%2B4%29%2BW%5E2
100+=+2W%5E2%2B4W%2B4 Divide through by 2 to simplify a bit.
50+=+W%5E2%2B2W%2B2 Subtract 50 from both sides.
W%5E2%2B2W-48+=+0 Solve this quadratic equation by factoring.
%28W-6%29%28W%2B8%29+=+0 Apply the zero product principle.
W-6+=+0 or W%2B8+=+0
If W-6+=+0 then W+=+6
If W%2B8+=+0 then W+=+-8 Discard this solution as the width, W, must be a positive value.
W+=+6
The width is 6 meters.
L+=+W%2B2
L+=+8
The length is 8 meters.
Check:
c%5E2+=+a%5E2%2Bb%5E2 Substitute c = 10, a = 8, and b = 6.
10%5E2+=+8%5E2%2B6%5E2
100+=+64%2B36
100+=+100 OK!