Question

If FH = 9x + 15 and GH = 5x + 4, then FG = ?

Answer 1

Answer:

FG = 39

Step-by-step explanation:

From the question given:

FH = 9x + 15

GH = 5x + 4

FG = ?

From the question given above, we can say that G is the midpoint of FH. This implies that:

FH = FG + GH

With the above idea in mind, we can obtain FG as follow:

FH = 9x + 15

GH = 5x + 4

FG = ?

FH = FG + GH

9x + 15 = FG + 5x + 4

Rearrange

FG = 9x + 15 - 5x - 4

FG = 9x - 5x + 15 - 4

FG = 4x + 11

Next, we shall determine the value of x. This can be obtained as follow:

Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e

FG = GH

With the above idea in mind, we can obtain the value of x as follow:

FG = 4x + 11

GH = 5x + 4

FG = GH

4x + 11 = 5x + 4

Collect like terms

11 - 4 = 5x - 4

7 = x

x = 7

Thus, we can obtain the value of FG as follow:

FG = 4x + 11

x = 7

FG = 4x + 11

FG = 4(7) + 11

FG = 28 + 11

FG = 39

***Check ***

FH = 9x + 15

x = 7

FH = 9(7) + 15 = 63 + 15 = 78

GH = 5x + 4

x = 7

GH = 5(7) + 4 = 35 + 4 = 39

FG = 4x + 11

x = 7

FG = 4(7) + 11 = 28 + 11 = 39

FH = FG + GH

FH = 78

FG = 39

GH = 39

FH = FG + GH

78 = 39 + 39

78 = 78