Question

Point G is the midpoint of RH. It is known that RG = 7x - 23 and RH = 6x + 90. Find the value of GH

Answer 1

96

Explanation:

Drawing a picture helps to think this problem through. 2(7x-23)=6x+90 by midpoint theorem. Solve this equation.

14x-46=6x+90

8x=136

x=17

Substitute x in the equation for RG. 7(17)-23.

7x17=119

119-23=96

Answer 2

GH = 96

Explanation:

Since G is at the midpoint of RH then RG = SH and

GH = 7x - 23

Thus

RG + GH = RH ← substitute values

7x - 23 + 7x - 23 = 6x + 90

14x - 46 = 6x + 90 ( subtract 6x from both sides )

8x - 46 = 90 ( add 46 to both sides )

8x = 136 ( divide both sides by 8 )

x = 17

Hence

GH = 7x - 23 = (7 × 17) - 23 = 119 - 23 = 96