Question

Use the image to answer the question.

A line divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse.

Use the geometric mean to find the value of x, which is the shortest leg of the large triangle. Round to the nearest tenth, if necessary.

(1 point)
Responses

8
8

4.9
4.9

15
15

2.8

Answer 1

8

Reason: by the geometric-mean relation for a right triangle split by the altitude to the hypotenuse, the leg x satisfies x^2 = (hypotenuse)(adjacent hypotenuse segment). That gives x^2 = 64, so x = 8.