Question

The line forms a second right angle, marked by a small square, where it meets the hypotenuse, and it divides the hypotenuse into 3 and 5. The short leg of the triangle is labeled x.

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

4.9
4.9

15
15

2.8
2.8

8

Answer 1

Use the altitude-to-hypotenuse relation: each leg is the geometric mean of the hypotenuse and the adjacent hypotenuse segment. The hypotenuse = 3+5 = 8, so the short leg x = sqrt(3·8) = sqrt(24) ≈ 4.9.

Answer: 4.9