Question

Use the image to answer the question.

A line divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse.
▶Click for Long Desc

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

15
15

2.8
2.8

4.9

Answer 1

15

Reason: If the altitude to the hypotenuse splits it into lengths 9 and 16, the short leg x satisfies x^2 = (hypotenuse)(adjacent segment) = 25·9, so x = sqrt(225) = 15.