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

Answer:

$x=2$

Step-by-step 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:

$\frac{4x+2}{2x+16}=\frac{18}{36}$

Simplify:

$\frac{4x+2}{2x+16}=\frac{1}{2}$

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:

$x=\frac{12}{6}$

Simplify:

$x=2$