Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is clear that triangle LMN is a right angled triangle.
According to Pythagoras theorem: In a right angled triangle
[tex]hypotenuse^2=perpendicular^2+base^2[/tex]
In triangle LMN,
[tex]LN^2=LM^2+MN^2[/tex]
[tex](\sqrt{20})^2=x^2+(x-2)^2[/tex]
[tex]20=x^2+x^2-4x+4[/tex]
[tex]20=2x^2-4x+4[/tex]
Subtract 20 from both sides.
[tex]0=2x^2-4x+4-20[/tex]
[tex]0=2x^2-4x-16[/tex]
Taking out common factors.
[tex]0=2(x^2-2x-8)[/tex]
Splitting the middle term we get
[tex]0=2(x^2-4x+2x-8)[/tex]
[tex]0=2(x(x-4)+2(x-4))[/tex]
[tex]0=2(x-4)(x+2)[/tex]
Using zero product property we get
[tex]x-4=0\Rightarrow x=4[/tex]
[tex]x+2=0\Rightarrow x=-2[/tex]
The value of can not be negative because side of a triangle is always positive. So, the value of x is 4.
Therefore the correct option is B.
