Question

What is the value of x

Answer 1

12

Explanation:

The first step that I would take is fine the 3,6, triangle using the pythagoras theorem.

`√(9+36) =√(45)`

We should also set a variable for the last side we haven't figured out yet (I will refer to it as y)

so here is what we know

`45+y^2=(3+x)^2\\\\x^2+36=y^2`

notice how both equations have
`y^2` this should give you a hint as to what to do

`y^2=(3+x)^2-45\\\\y^2=x^2+36`

therefore

`(3+x)^2-45=x^2+36`

now solve for x

`(3+x)^2-45=x^2+36\\\\x^2+6x+9-45=x^2+36\\\\x^2+6x-36=x^2+36\\\\6x=72\\\\x=12`