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Question

ABCD is a rectangle having length (x+1) and breadth (x1) . If P, Q, R and S are the mid-points of side AB, BC, CD and DA respectively, then the perimeter of the quadrilateral PQRS is

A
4a(x21)x
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B
4a(x21)2
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C
24x2+1
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D
22(x2+1)
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Solution

The correct option is D 22(x2+1)
From given, we have,

In APS

SP2=AP2+AS2

=(x+12)2+(x12)2

=x2+12

SP=x2+12

but, we have,

SP=PQ=QR=RS

Perimeter of PQRS=4(SP)=4×x2+12

=22(x2+1)

1476199_1424658_ans_7694d37a2cbc4bb384bf676d03d12dd9.png

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