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.
