Question

B is the midpoint of AC. Find the length of AC.

Answer 1

The length of AC would be 168.

Explanation:

A midpoint of the line segment is the point that is halfway between the endpoints of the line segment.

Since B is the midpoint of AC, we have AB=BC

here,
`AB=5\cdot x+9` and
`BC=8\cdot x-36`

AC=AB+BC

AC=BC+BC

`AC=2\cdot BC`

∴
`AC=2(8x-36)=16x-72` ....(1)

to find the length of AC we have to find the value of x from the given condition i.e, AB=BC

`5x+9=8x-36`

Combine like terms:

`9+36=8x-5x`

`45=3x`

∴
`x=15`

Now, putting the value of x in (1) we get,

AC
`=16x-72`

`AC=16\cdot 15 -72`=
`240-72`=168

Therefore, the length of AC is 168.