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Question

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

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Solution

the fact that a rectangular pond has to be constructed in the centre of a rectangular lawn of dimensions 50m×40m So, the distance between pond and lawn would be same around the pond. Say x m.


Now, length of rectangular lawn (l1)=50m
and breadth of rectangular lawn (b1)=40m
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 =1184m2​​​​​​​


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 = 502x=502(8)=5016=34m
and breadth of pond = 402x=402(8)=4016=24m
Hence, required length and breadth of pond are 34 m and 24 m, respectively.


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