Question

In triangle ABC,PBllBC.If AP=3.5cm,PB=7cm and PQ=4.5cm,find BC.

Answer 1

Answer:

BC = 13.5cm

Step-by-step explanation: Given,

In ΔABC,

PQ//BC, AP = 3.5cm, PB = 7cm, PQ = 4.5cm

To find - BC

Proof - Since PQ//BC

AP/PB = AQ/QC

Now, In ΔABC and ΔAPQ,

∠A = ∠A (common)

AP/PB = AQ/QC (PQ//BC)

∴ By SAS similarity,

ΔABC ~ ΔAPQ

∴ AP/AB = AQ/ AC = PQ/BC (corresponding sides of similar triangles are proportional)

AP/AB = PQ/BC

3.5 / (7+3.5) = 4.5/BC

3.5(BC) = 4.5(7+3.5)

3.5BC = 4.5(10.5)

BC = 47.25 ÷ 3.5

BC = 13.5cm

Answer 2

Answer:

In triangle ABC,PBllBC.If AP=3.5cm,PB=7cm and PQ=4.5cm,find BC.

BC=13.5cm