Question

Given: triangle FOG and triangle BAT angle G is congruent to angle T, FG = 5x, FO = 42, AB = 14, and AT = x + 12. Find the length of FG.

a) 30
b) 25
c) 20
d) 15

Answer 1

To find the length of FG in triangle FOG, set up a proportion between FG/FO and AB/AC. Solve the proportion to find x, then substitute x into FG = 5x.

Step-by-step explanation:

To find the length of FG in triangle FOG, we can use the fact that angle G is congruent to angle T. Since AB = 14 and AT = x + 12, and AC = 3R, we can set up a proportion:

(FG/FO) = (AB/AC)

(5x/42) = (14/3R)

Now we can solve for FG:

5x * 3R = 14 * 42

15xR = 588

Dividing both sides by 15:

xR = 39.2

Since R = x + 12, we can substitute:

(x + 12)x = 39.2

x^2 + 12x - 39.2 = 0

Using the quadratic formula, we find that x ≈ 2.8

Substituting x back into the equation FG = 5x:

FG = 5(2.8) ≈ 14

Therefore, the length of FG is approximately 14. The correct answer is (d) 15.