Question

A APQ ~ AABC, AP=2.4cm, AQ = 2 cm, QC = 3,
and Be = 6oom, find the length of AB​

Answer 1

Answer:

Given :  AP = 2.4 cm, AQ = 2 cm, QC = 3 cm, and BC = 6 cm.

By using Basic proportionality theorem,

AP/PB = AQ/QC

2.4/ PB = 2/3

2PB = 2.4 x 3  

PB = (2.4×3) /2  

PB = 1.2 × 3  

PB = 3.6 cm

Now, AB = AP + PB

AB = 2.4 + 3.6

AB = 6 cm

In Δ APQ and Δ ABC,

∠APQ =∠ABC  (corresponding angles)

[PQ || BC, AB is transversal]

∠AQP =∠ACB  (corresponding angles)

[PQ || BC, AC is transversal]

Δ APQ  ~ Δ ABC (AA similarity)

Therefore,  AP/AB = PQ/BC = AQ/AC

[In similar triangles corresponding sides are proportional]

AP/ AB = PQ/BC

2.4/ 6 = PQ/6

PQ = 2.4 cm

Hence, AB = 6 cm  and PQ = 2.4 cm.

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Step-by-step explanation:

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refer the attachment