Question

The figure below shows a triangular lawn labeled PQR. There are two fences, AB and BC.

What is the total length of the fence AB and BC?
56 feet
72 feet
100 feet
128 feet

Answer 1

In PQR and BQC,
Q=Q (common)
P=B (corr. angle, PR//BC)
Q=C (corr. angle, PR//BC)
PQR is similar to BQC (A.A.A.)
QP/QB=QR/QC
100/60 = 140/QC
QC= 84
RC=RQ-CQ= 140-84 = 56
PR/BC = PQ/BQ
120/BC = 100/60
BC=72

AB=RC (property of //gram)
= 56

AB+BC = 56+72=128 feet