Question

Find the value of x. The image is of a triangle with its base marked as 2x+16. A segment of length 4x+2, parallel to the base bisects the other two sides into lengths 18;18 and 23;23.

Answer 1

`x=2`

Explanation:

The two triangles are similar. So that means it's corresponding sides are proportional.

So this means we can find x using the equation:

`(4x+2)/(2x+16)=(18)/(36)`

Simplify:

`(4x+2)/(2x+16)=(1)/(2)`

Cross multiply:

`2(4x+2)=1(2x+16)`

Distribute/multiply:

`8x+4=2x+16`

Subtract
`2x` on both sides:

`6x+4=16`

Subtract
`4` on both sides:

`6x=12`

Divide both sides by 6:

`x=(12)/(6)`

Simplify:

`x=2`