Question 184007: One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters then what are the length of the sides. Answer by solver91311(24713) (Show Source):
The diagonal of a rectangle forms a right triangle with two of the sides. So if one of the sides is a, another side is b, and the diagonal is c, the Pythagorean Theorem says:
Since we know that one of the sides of the rectangle is 2 meters longer than the other we can say one is a and the other is a + 2. That, plus knowing that the diagonal is 10 lets us write:
Just solve the quadratic by factoring. One of the roots will be negative. Exclude this absurd result as an extraneous root. The positive root will be the width of the rectangle. Add 2 to get the length.
