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?

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) (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 () 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:
Substitute L = W+2

Divide through by 2 to simplify a bit.
Subtract 50 from both sides.
Solve this quadratic equation by factoring.
Apply the zero product principle.
or
If then
If then Discard this solution as the width, W, must be a positive value.

The width is 6 meters.

The length is 8 meters.
Check:
Substitute c = 10, a = 8, and b = 6.

OK!
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