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Question

The dimensions of a rectangle ABCD are 51 cm×25 cm. A trapezium with its parallel sides QC and PD in the ratio 9:8, is cut of from the rectangle as shown in figure. If the area of the trapezium PQCD is 56 the area of the rectangle, find the lengths QC and PD.


A

QC = 81cm, PD = 72cm

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B

QC = 36cm, PD = 32cm

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C

QC = 45cm, PD = 40cm

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D

QC = 54cm, PD = 48cm

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Solution

The correct option is C

QC = 45cm, PD = 40cm


ABCD is a rectangle in which AB = 51cm and BC = 25 cm

Since parallel sides QC and PD are in the ratio 9:8, so let QC=9x and PD=8x.

Now area of trapezium PQCD

=12×(9x+8x)×25 cm2

=12×17x×25

Area of rectangle ABCD

=BC×CD=51×25

It is given that area of trapezium PQCD

=56×Area of rectangle ABCD.

12×17x×25=56×51×25

x=56×51×25×2×117×25=5

Hence the length QC=9x=9×5=45cm. and the length PD=8x=8×5=40cm.


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