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Question

In the centre of a rectangular lawn of dimensions 50 m×40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.


A

30 m and 20 m

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B

40 m and 30 m

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C

35 m and 20 m

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D

34 m and 24 m

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Solution

The correct option is D

34 m and 24 m


Given that a rectangular pond has to be constructed in the centre of a rectangular lawn of dimensions 50m×40m Let the width of the lawn be x metres.


Now, length of rectangular lawn (l1)=50 m
and breadth of rectangular lawn (b1)=40 m
Length of rectangular pond (l2)=50(x+x)=502x
and breadth of rectangular pond (b2)=40(x+x)=402x
Also, area of the grass surrounding the pond = 1184 m2
Area of rectangular lawn - Area of rectangular pond = Area of grass surrounding the pond.
l1×b1l2×b2=1184[() area of rectangle=length×breadth]
50×40(502x)(402x)=11842000(200080x100x+4x2)=118480x+100x4x2=11844x2180x+1184=0x245x+296=0x237x8x+296=0 [by splitting the middle term]
x(x37)8(x37)=0(x37)(x8)=0
x = 8
[At x = 37, length and breadth of pond are -24 and -34, respectively but length and breadth cannot be negative. So, x = 37 cannot be possible]
Length of pond = 50 - 2x = 50 - 2(8) = 50 - 16 = 34 m
and breadth of pond = 40 - 2x = 40 - 2(8) = 40 - 16 = 24 m
Hence, required length and breadth of pond are 34 m and 24 m, respectively.


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