Question

Point Q is on line segment PR. Given QR = 3x, PQ = x + 6, and

PR = 5x – 4, determine the numerical length of PQ.

Answer 1

Given:

Point Q is on line segment PR.

QR = 3x, PQ = x + 6, and PR = 5x – 4.

To find:

The numerical length of PQ.

Solution:

Since, point Q is on line segment PR, so by segment addition property, we get

`PR=PQ+QR`

`5x-4=(x+6)+3x`

`5x-4=4x+6`

`5x-4x=4+6`

`x=10`

The value of x is 10.

Now,

`PQ=x+6`

Putting x=10, we get

`PQ=10+6`

`PQ=16`

Therefore, the numerical length of PQ is 16 units.