Question

pqrs is a trapezium pq//sr qr=rs and angle = 90 .if qr=24 cm and ps = 25 then find the length of pq

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Answer 1

Answer:

Given: PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm

Draw a perpendicular from P on SR at X, and from Q on SR at Y

thus, PX=QY=diameter

Now, In △PSX and △QRY

PS=QR (Given)

∠PXS=∠QYR (Each 90)

PX=QY (distance between parallel lines)

hence, △PSX≅△QRY (SAS rule)

thus, SX=RY=

2

32−18

​

=7

Now, In △PSX, Using Pythagoras Theorem,

PS

2

=PX

2

+SX

2

25

2

=PX

2

+7

2

PX=24 cm

Step-by-step explanation: