Question

Use the geometric mean to find the value of x, which is the shortest leg of the large triangle. Round the nearest tenth, if necessary. The numbers are 3 and 5 and x. A. 4.9. B. 8. C. 15. D. 2.8.

Answer 1

If the altitude to the hypotenuse splits it into 3 and 5, then the whole hypotenuse is 3+5 = 8. For a right triangle with altitude to the hypotenuse, the short leg x satisfies

x^2 = (hypotenuse)(adjacent segment) = 8·3 = 24.

So x = sqrt(24) ≈ 4.9.

Answer: A.