Answer:
x = 10 , EF = 8 , FG = 15.
Explanation:
Given : If EF = 2x – 12, FG = 3x – 15, and EG = 23.
To find : find the values of x, EF, and FG.
Solution : We have given EF = 2x – 12, FG = 3x – 15, and EG = 23.
Let the line E ___F___G.
Here F is the mid point of EG . ( mid point divide the line EG cut the line EG in two equal parts)
We can say EF = FG.
EF + FG = EG -------(1)
Plug tha values EF = 2x -12 and FG = 3x - 15 , EG = 23 in equation (1).
2x - 12 + 3x -15 = 23 .
On combine like terms
2x + 3x -12 -15 = 23 .
5x - 27 + 23 .
on adding both side by 27.
5x = 23 +27.
5x = 50 .
On dividing both sides by 5.
x = 10.
Them, EF = 2 (10) -12
20 -12
EF = 8
FG = 3 (10) -15 .
FG = 30 -15 .
FG = 15.
EG = 5 +18 = 23 .
Therefore, x = 10 , EF = 8 , FG = 15.