Question

In the figure below, the segment is parallel to one side of the triangle. Find the value of x

Answer 1

16/22 = 8/11
8/11 = x/x+7
8x+56 = 11x
11x-8x = 56
3x = 56
x = 56/3
=18 2/3

Answer 2

`x=18{(2)/(3)}`

Explanation:

It is given that the segment is parallel to one side of the triangle, therefore using the proportionality theorem, we get

`(x)/(x+x+7)=(16)/(16+22)`

⇒
`(x)/(2x+7)=(16)/(38)`

⇒
`(x)/(2x+7)=(8)/(19)`

Upon cross multiplying, we have

⇒
`19x=16x+56`

⇒
`3x=56`

⇒
`x=18{(2)/(3)}`

Thus, the value of x is
`18{(2)/(3)}`.

Hence, option B is correct.