Question

What is the value of x and the length of segment DE?

StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)

x = _____
Length of = ___units

Answer 1

Explanation:

This is a geometric means problem involving the height of 9. 9 is the geometric mean because it is the height of both ΔCFD and ΔEFD. Set up the problem accordingly:

`(5)/(9)=(9)/(2x+3)` and cross multiply:

81 = 5(2x + 3) and

81 = 10x + 15 and

66 = 10x so

x = 6.6

Now we will plug that value in for x to find the length of DE:

2(6.6) + 3 = 16.2 units