The length of one leg of a right triangle is 1 centimeter more than the length of the other leg. The length of the hypotenuse is 5 centimeters. Find the lengths of the two legs.
A) 3 cm, 4 cm
B) 1 cm, 2 cm
C) 6 cm, 5 cm
D) 5 cm, 6 cm

Question

Quizplus · Accepted Answer

Let's denote the length of one leg by x and the length of the other leg by x+1.
Using Pythagoras' theorem, we have:
x^2 + (x+1)^2 = 5^2
x^2 + x^2 + 2x + 1 = 25
2x^2 + 2x - 24 = 0
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 (discard this solution as it is not a positive length) or x = 3

If x = 3, then the other leg is x+1 = 4. These lengths satisfy the condition of being the legs of a right triangle and the hypotenuse being 5 centimeters long. Therefore, the answer is A, 3 cm and 4 cm.

The Length of One Leg of a Right Triangle Is