Question

The two triangles are similar. What is the value of x?

Answer 1

`x=10`

Explanation:

So we have two triangles with `3x,20,h` and `4x+2,28,H`
where the `h`s are the hypotheses.

Let's find the common ratio.
Remember: we divide two corresponding sides.
The known side lengths are `20` and `28`, and they correspond to each other.

Therefore, the ratio of the side lengths of the smaller triangle to the larger one is: `20/28=>5/7`

This means that the ratio of all the corresponding sides of the two triangles(from the smaller one to the larger one) has to equal `5/7`.

Therefore, `(3x)/(4x+2)=5/7`
We solve this proportion.

`(3x)/(4x+2)=5/7`
`7(3x)=5(4x+2)`
`21x=20x+10`
`x=10`
That is the answer!