Question

In the given diagram, if AP = 15 cm, AQ = 24 cm and PB + QC = 26 cm, find QC – PB, given PQ || BC.

Answer 1

QC - PB = 6

Explanation:

Given PQ is parallel to BC then it divides the sides proportionally, that is

`(AP)/(AQ)` =
`(PB)/(QC)` =
`(15)/(24)` =
`(5)/(8)` , then

`(PB)/(QC)` =
`(5)/(8)` ( cross- multiply )

8PB = 5QC → *

Given PB + QC = 26 , then

PB = 26 - QC

Substitute into *

8(26 - QC) = 5QC ← distribute left side

208 - 8QC = 5QC ( subtract 5QC from both sides )

208 - 13QC = 0 ( subtract 208 from both sides )

- 13QC = - 208 ( divide both sides by - 13 )

QC = 16

Thus PB = 26 - QC = 26 - 16 = 10

QC - PB = 16 - 10 = 6