Question

Find the unknown side length, x. Write your answer in simplest radical form.

Answer 1

i hope this helps you

Answer 2

x=4

Explanation:

It is given that LMN is a right angled triangle which is right angled at M, therefore using the Pythagoras theorem, we have

`(NL)^(2)=(MN)^(2)+(ML)^(2)`

Substituting the given values, we get

`(√(20))^(2)=(x-2)^(2)+x^(2)`

`20=x^2+4-4x+x^2`

`20=2x^2-4x+4`

`2x^2-4x-16=0`

`x^2-2x-8=0`

`x^2-4x+2x-8=0`

`x(x-4)+2(x-4)=0`

`(x+2)(x-4)=0`

Thus, the value of x will be equal to 4 because x cannot take the negative value.