Question

What is the length of FG?

(Picture of Question Below!)

A. 1.2
B. 3
C. 3.6
D. 4 ( IT IS NOT D!)
E. 6

Answer 1

9514 1404 393

Answer:

C. 3.6

Explanation:

AC = FA + FC = 4+6 = 10

AC is the hypotenuse of right triangle ABC, which has leg BC = 8. Then the length of AB is given by the Pythagorean theorem as ...

AB² +BC² = AC²

AB = √(10² -8²) = 6

The side lengths of these similar triangles are proportional, so you have ...

FG/FC = AB/AC

FG = FC(AB/AC) = 6(6/10)

FG = 3.6