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

lengths are 3 5 and x

Answer 1

The hypotenuse is 3 + 5 = 8. For the leg adjacent to the 3-segment, a^2 = (hypotenuse)(adjacent segment) so
x = a = sqrt(8·3) = sqrt(24) ≈ 4.9.
Thus the shortest leg is 4.9.