Question

Use the image to answer the question.

A line, x, divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse. The line x forms a second right angle, marked by a small square, where it meets the hypotenuse, and it divides the hypotenuse into 5 and 12.

Use the geometric mean to solve for the value of x.

(1 point)
Responses

60
60

2.65
2.65

17
17

7.75

Answer 1

The altitude from the right angle to the hypotenuse satisfies x^2 = (5)(12). So x = sqrt(60) = 2√15 ≈ 7.75.

Answer: 7.75.