Question

Which value of x would make LK ∥ OM? x = 2 x = 2.4 x = 4.8 x = 8

Answer 1

Answer:

x=8

Step-by-step explanation:

The figure is shown in the attached figure.

We have, LK║OM. We need to find the value of x.

It is based on side-splitter theorem. If a line is parallel to third side of a triangle, then the points that intersects the two lines, it divides proportionally.

Using it in given problem. So,

$\dfrac{\text{NK}}{\text{KM}}=\dfrac{\text{NL}}{\text{LO}}$

Nk = x+2, KM = x-3, NL = x and LO = x-4

So,

$\dfrac{x+2}{x-3}=\dfrac{x}{x-4}$

Cross multiplying, we get :

$(x+2)(x-4)=x(x-3)\\\\x^2-4x+2x-8=x^2-3x\\\\-2x+3x=8\\\\x=8$

So, the value of x is 8.