Question

In the following figure, ABCD to a trapezium
with AB || DC. If AB = 9 cm, DC = 18 cm,
CF = 13.5 cm, AP 6 cm and BE=15 cm,
Calculate:
1. EC
2. AF
3. PE

Answer 1

Step-by-step explanation:

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Understanding Quadrilaterals

Kinds of Quadrilateral

In the following figure, AB...

MATHS

In the following figure, ABCD to a trapezium with AB∥DC. If AB=9 cm, DC= 18 cm, CF= 13.5 cm, AP= 6 cm and

BE=15 cm. Calculate PE

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ANSWER

Given ABCD is trapezium, AB∥DC

⇒AB=9 cm,DC=18 cm,CF=13.5 cm,AP=6 cm,BE=15 cm

Consider △APD and △BPE

⇒∠APD=∠BPE ( Vertically opposite angles )

⇒∠ADP=∠EBP ( Alternate angles since DC∥AB and AD∥BC )

∴△APD≅△BPE

∴

PB

PA

=

PE

PD

=

BE

AD

⇒

BP

6

=

PE

PD

=

15

AD

⇒

6

6

=

15

AD

⇒AD=15 cm.

∴ From the equations

⇒PE=

18

15×6

=4.8 cm.

Hence, the answer is 4.8 cm.