Question

Find the value of x.

A.
2
B.
4
C.
6
D.
8



Please select the best answer from the choices provided

Answer 1

Explanation:

Answer 2

The correct option is B.

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

`hypotenuse^2=perpendicular^2+base^2`

In triangle LMN,

`LN^2=LM^2+MN^2`

`(√(20))^2=x^2+(x-2)^2`

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

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

Subtract 20 from both sides.

`0=2x^2-4x+4-20`

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

Taking out common factors.

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

Splitting the middle term we get

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

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

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

Using zero product property we get

`x-4=0\Rightarrow x=4`

`x+2=0\Rightarrow x=-2`

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.