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
[tex](NL)^{2}=(MN)^{2}+(ML)^{2}[/tex]
Substituting the given values, we get
[tex](\sqrt{20})^{2}=(x-2)^{2}+x^{2}[/tex]
[tex]20=x^2+4-4x+x^2[/tex]
[tex]20=2x^2-4x+4[/tex]
[tex]2x^2-4x-16=0[/tex]
[tex]x^2-2x-8=0[/tex]
[tex]x^2-4x+2x-8=0[/tex]
[tex]x(x-4)+2(x-4)=0[/tex]
[tex](x+2)(x-4)=0[/tex]
Thus, the value of x will be equal to 4 because x cannot take the negative value.
