Solve.
-One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle.
A)12 in., 33 in., 36 in
B)14 in., 35 in., 40 in
C)15 in., 36 in., 39 in.
D)16 in., 37 in., 40 in

Question

Quizplus · Accepted Answer

Let the smaller leg be x. Then the longer leg is x + 21 and the hypotenuse is x + 24.
Using the Pythagorean theorem, we can write:
x^2 + (x + 21)^2 = (x + 24)^2
Expanding and simplifying, we get:
2x^2 + 42x - 375 = 0
Factoring, we get:
(2x - 15)(x + 25) = 0
Since the length of a side of a triangle must be positive, we reject the solution x = -25.
Therefore, x = 15, and the lengths of the sides are:
smaller leg = 15 inches
longer leg = 36 inches (15 + 21)
hypotenuse = 39 inches (15 + 24)
So the best choice is C. Let x be the length of the smaller leg. Then the longer leg is x + 21, and the hypotenuse is x + 24. Using the Pythagorean Theorem, we have:
x^2 + (x+21)^2 = (x+24)^2
Expanding and simplifying:
2x^2 + 42x - 345 = 0
Using the quadratic formula:
x = (-42 ± sqrt(42^2 - 4(2)(-345))) / (2(2))
x = (-42 ± 48) / 4
x = 1.5 or x = -23.25 (discarding the negative solution)
So the smaller leg is 15 inches (choice C), the longer leg is 36 inches, and the hypotenuse is 39 inches.

Solve. -One Leg of a Right Triangle Is 21 Inches Longer