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

2.8
2.8

15
15

8
8
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Answer 1

When the altitude to the hypotenuse divides it into 3 and 5, the hypotenuse is 3+5 = 8. For the shorter leg x, the geometric-mean relation is x^2 = (hypotenuse)(adjacent segment) = 8·3 = 24. So x = √24 ≈ 4.9.

Answer: 4.9