Question

I have to solve for X. someone pleaseeeee walk me through this

Answer 1

x = 12

Explanation:

Because the two sides are parallel as shown, the two triangles are similar.

The lengths of corresponding sides of similar triangles are proportional.

Look at the large triangle first.

The upper side of the large triangle measures x + x + 6 = 2x + 6.

The lower side of the large triangle measures 8 + 12 = 20.

Now look at the small triangle at the right.

The upper side measures x + 6.

The lower side measures 12.

The corresponding sides of the large triangle to the small triangle are:

2x + 6 corresponds to x + 6.

20 corresponds to 12.

Since the lengths of the corresponding sides are proportional, we set up a proportion.

`(2x + 6)/(x + 6) = (20)/(12)`

Cross multiply.

`12(2x + 6) = 20(x + 6)`

Divide both sides by 4.

`3(2x + 6) = 5(x + 6)`

`6x + 18 = 5x + 30`

Subtract 5x from both sides. Subtract 18 from both sides.

`6x - 5x + 18 - 18 = 5x - 5x + 30 - 18`

`x = 12`