Question

Point Q is the midpoint of GH. GQ = 2x + 3, and GH = 5x - 5. What is the length of GQ?

Enter your answer in the box.

Answer 1

`\displaystyle 25 = GQ`

Step-by-step Step-by-step explanation:

If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:

`\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}`

Plug the result into the expression for the length of GQ to get twenty-five units.

I am joyous to assist you at any time.