Question

If g is the midpoint of FH, FG=14x+25 and gh is 73-2x find fh

Answer 1

Set the expressions for FG and GH equal, solve for x, then calculate the length of one segment and double it to find FH, which is 134 units.

Step-by-step explanation:

If G is the midpoint of FH, the segments FG and GH are equal in length.

We are given that FG equals 14x + 25 and GH equals 73 - 2x.

To find the length of FH, we set the two expressions equal to each other since FG = GH.

• 14x + 25 = 73 - 2x
• 14x + 2x = 73 - 25
• 16x = 48
• x = 3

Now that we found x, we can calculate the length of either FG or GH and then double it to find FH, because FH is twice the length of either FG or GH (since G is the midpoint).

• FG = 14(3) + 25 = 42 + 25 = 67
• FH = 2 × FG = 2 × 67 = 134

Therefore, the length of FH is 134 units.