Question

L
N
(x-4) in. O
(x-3) in.
(x + 2) in.
x in.
K
Which value of x would make NO || KJ?
1
6
08
O 10

Answer 1

Answer:

x = 8

Step-by-step explanation:

$\sf If\:\: \overline{NO} \parallel \overline{KJ}\:\:then\:\: \triangle LNO \sim\triangle LKJ$

Therefore:

$\implies \sf \overline{LN} : \overline{LO} = \overline{LK} : \overline{LJ}$

$\implies (x-3):(x-4)=(x-3)+(x+2):(x-4)+x$

$\implies \dfrac{x-3}{x-4}=\dfrac{2x-1}{2x-4}$

$\implies (x-3)(2x-4)=(2x-1)(x-4)$

$\implies 2x^2-10x+12=2x^2-9x+4$

$\implies -10x+12=-9x+4$

$\implies 12=x+4$

$\implies x=8$