Question

9) In ∆ ABC, line PQ || side BC, AP = 3, BP=6, AQ= 5 then the value of CQ is __________ *
2 points

Answer 1

Step-by-step explanation:

AP AQ

___ = ____

BP QC

3 5

__ = ____

6 QC

5 × 6

QC = _____

3

QC = 5 × 2

QC = 10

Hope this Helps.

Answer 2

Answer:

The length of CQ is 5 units

Step-by-step explanation:

Given:

PQ || BC

AP = 3

BP = 6

AQ = 5

Solution:

In ∆ ABC and ∆ APQ,

∠A = ∠A                             (common in both)

∠ABC = ∠APQ                   (corresponding angles)

∠ACB = ∠AQP                   (corresponding angles)

Therefore, ∆ ABC ≈ ∆ APQ     (by AAA)

=> $\frac{AP}{AB}$ = $\frac{AQ}{AC}$ = $\frac{PQ}{BC}$

On substitution in $\frac{AP}{AB}$ = $\frac{AQ}{AC}$

=> $\frac{3}{6}$ = $\frac{5}{AC}$

=> AC = 10

We know AC = AQ + QC

=> 10 = 5 + QC

=> QC = 10 - 5

          = 5

Therefore, the length of CQ is 5 units