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

x = 8

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 (x-3)/(x-4)=(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`