Solve.
-The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the triangle.
A)20 ft, 48 ft, 52 ft
B)30 ft, 68 ft, 82 ft
C)15 ft, 36 ft, 39 ft
D)18 ft, 44 ft, 46 ft

Question

Quizplus · Accepted Answer

The hypotenuse is 8 feet less than three times the shorter leg, so the hypotenuse is 3x - 8. The longer leg is 8 feet more than twice the shorter leg, so the longer leg is 2x + 8. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, so we have (3x - 8)^2 = x^2 + (2x + 8)^2. Expanding and simplifying, we get 9x^2 - 48x + 64 = x^2 + 4x^2 + 32x + 64. Combining like terms, we get 4x^2 - 80x = 0. Factoring out 4x, we get 4x(x - 20) = 0. So x = 0 or x = 20. Since the length of a side cannot be 0, we have x = 20. Therefore, the shorter leg is 20 feet, the longer leg is 48 feet, and the hypotenuse is 52 feet.

Solve. -The Hypotenuse of a Right Triangle Is 8 Feet Less