The hypotenuse of a right triangle is 10 inches. The lengths of the two legs are given by two consecutive even integers. Find the lengths of the two legs.
A)8 inches and 10 inches
B)4 inches and 6 inches
C)2 inches and 4 inches
D)6 inches and 8 inches
E)none of these

Question

Quizplus · Accepted Answer

Let x be the length of the shorter leg. Then the length of the longer leg is x + 2. According to the Pythagorean theorem, we have x^2 + (x+2)^2 = 10^2. Simplifying the equation gives 2x^2 + 4x - 84 = 0. Dividing both sides by 2, we get x^2 + 2x - 42 = 0. Factoring the quadratic equation gives (x+7)(x-5) = 0. Since x has to be an even integer, the only possible solution is x = 6. Therefore, the lengths of the two legs are 6 inches and 8 inches.

The Hypotenuse of a Right Triangle Is 10 Inches