Question

How do you solve for x?

Answer 1

Explanation:

Using little bottom triangle:

`y^2=10^2+20^2` (Pythagoras Theorem)

`y^2=500`

Using big triangle:

`y^2+z^2=(10+x)^2` (Pythagoras Theorem)

`500+z^2=(10+x)^2` (Since we know
`y^2=500`)

`500+z^2=x^2+20x+100`

`z^2=x^2+20x-400`
`(a)`

Using little top triangle:

`z^2=x^2+20^2` (Pythagoras Theorem)

`z^2=x^2+400`
`(b)`

Substitute
`(a)` into
`(b)`:

`x^2+20x-400=x^2+400` (since we know both sides
`=z^2`)

`20x=800`

`x=40`