Question

Which value of x would make NO IKI

?
K
(x + 2) in
o 1
N
(x - 3) in
06
o 8
x-4) in 0
x in
o 10
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Answer 1

`\boxed{x = 8}`

Explanation:

For NO ║ KJ, The two triangles must be similar and their sides must be proportional.

So, the proportion of their sides is:

=>
`(x-4)/(x) = (x-3)/(x+2)`

Cross Multiplying

`\sf x (x-3)= (x-4)(x+2)\\Multiplying\\x^2-3x = x^2+2x-4x-8\\x^2-3x = x^2-2x-8\\Subtracting\ x^2\ to \ both \ sides\\ -3x = -2x -8\\Adding \ 2x\ to\ both\ sides\\-3x+2x = -8\\-x = -8\\`

x = 8

So, For x = 8, NO will be parallel to KJ.