Question

FH = 56, FG = 2x - 5, and GH = 3x + 1. Find the value of x and FG.

Answer 1

The value of x is 12, and the length of segment FG is 19 units.

Step-by-step explanation:

To find the value of x and FG, we need to consider the relationship between FH, FG, and GH in a straight line. The segment FH is the entire length, so it is equal to the sum of FG and GH:
FH = FG + GH
56 = (2x - 5) + (3x + 1)

We can solve for x by combining like terms and then isolating x:

56 = 5x - 4
60 = 5x
x = 12

Now that we have the value of x, we can find FG:

FG = 2x - 5
FG = 2(12) - 5
FG = 24 - 5
FG = 19

Therefore, the value of x is 12 and FG is 19.