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Question

In the figure given below, AB||EF||CD, If AB =22.5 cm, EP =7.5 cm, PC =15 cm and DC =27 cm.

Calculate: (i) EF (ii) AC


A

EF = 12.5 cm, AC = 35.5 cm

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B

EF = 13.5 cm, AC = 37.5 cm

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C

EF = 13.5 cm, AC = 32 cm

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D

EF = 14 cm, AC = 37.5 cm

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Solution

The correct option is B

EF = 13.5 cm, AC = 37.5 cm


In the given figure.

AB||EF||CD

AB =22.5 cm, EP=7.5 cm

PC =15 cm and DC =27 cm

To calculate: (i) EF (ii)AC

In ΔDCP and ΔPEF

CPD=EPF (Vertically opp. angles)

DCP=PEF (Alternate angles)

ΔDCPΔPEF (AA axiom)

DCEF=CPPE27EF=157.5

EF=27×7.515=272=13.5cm

Similarly in ΔABC,EF||AB

ΔCDFΔACB

CEAC=EFAB

22.5AC=13.522.5

AC=22.5×22.513.5

=225×225135×10×10=37510cm

AC=37.5cm


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