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Question

Each side of a square ABCD is 12 cm. A point P lies on side CD such that area of ΔADP : area of trapezium ABCP = 2 : 3. Find DP.

A
9.6 cm
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B
8.5 cm
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C
9.6 m
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D
10.6 cm
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Solution

The correct option is A 9.6 cm
ABCD is a square with each side 12cm square.
P is a point on side CD.

Area of ADPArea of trapezium ABCP=23

Let CP=x
DP=12x

Now,
AreaofADP=12×AD×DP

=12×12×(12x)

=6(12x)

Area of trapezium ABCP=(AB+CP)2BC

=(12+x)212

=(12+x)6
Now,
6(12x)6(12+x)=23

=>363x=24+2x
=>3x2x=2436
=>5x=12
=>x=2.4

Length of CP = 2.4cm
Length of DP = 122.4cm
= 9.6cm

359342_197279_ans_6703b04ee16e4d8f9cb44b96237a5fce.png

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