The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).
A) 10.1, 8.1, 13.0
B) 10.1, 6.9, 13.0
C) 12.8, 10.8, 13.0
D) 11.0, 8.1, 13.0
E) 11.0, 6.9, 13.0

Question

The hypotenuse of a right triangle is 13.0, and one leg is 2.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth). ​
A) 10.1, 8.1, 13.0
B) 10.1, 6.9, 13.0
C) 12.8, 10.8, 13.0
D) 11.0, 8.1, 13.0
E) 11.0, 6.9, 13.0

Quizplus · Accepted Answer

Let x be the length of the shorter leg. Then the longer leg is x + 2. By the Pythagorean theorem, we have:x^2 + (x + 2)^2 = 13^2x^2 + x^2 + 4x + 4 = 1692x^2 + 4x - 165 = 0(x - 10.1)(x + 16.3) = 0x = 10.1Therefore, the dimensions of the figure are 10.1, 10.1 + 2 = 12.1, and 13.0.

The Hypotenuse of a Right Triangle Is 13