9) In ∆ ABC, line PQ || side BC, AP = 3, BP=6, AQ= 5 then the value of CQ is __________ *
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Step-by-step explanation:
AP AQ
___ = ____
BP QC
3 5
__ = ____
6 QC
5 × 6
QC = _____
3
QC = 5 × 2
QC = 10
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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)
=> = =
On substitution in =
=> =
=> AC = 10
We know AC = AQ + QC
=> 10 = 5 + QC
=> QC = 10 - 5
= 5
Therefore, the length of CQ is 5 units
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