Question

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

Answer 1

I hope this helps you

Answer 2

Answer:

x=4

Step-by-step 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

$(\sqrt{20})^{2}=(x-2)^{2}+x^{2}$

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

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

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

$x^2-2x-8=0$

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

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

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

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