wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
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.

Open in App
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.


flag
Suggest Corrections
thumbs-up
163
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Crystallization
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon