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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 Fig. 4.1]. Find the length and breadth of the pond.

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 Fig. 4.1]. Find the length and breadth of the pond.

Grade:10

2 Answers

aditya ketkar
40 Points
9 years ago
Here is the easiest explaination i could come up with -------------
 
Area of total lawn => 50 X 40 = 2000 m2
Area of grass => 1184 m2                           ---  (Given)
 
Therefore, area of pond => (Area of total lawn) – (Area of grass) = 2000 – 1184 = 816 m2
 
Here is a figure,
                        
                              ___________________________________________________________
                              |                                                                                                      |
                              |                                           GRASS                                                | 
                              |                          |--------------------------------------------|                               |
                              |                          |                                            |                               |
              40m          |                     x   |               POND                    |                               | 
                              |                          |                                            |                               | 
                              |                          |                                            |                               |
                              |                          |--------------------------------------------|                               |
                              |                                             y                                                        |
                              |                                                                                                       |
                              |___________________________________________________________|
                                                                            50m
 
 
Now,  let the length of sides of pond be x and y,
 
therefore,
 
x * y = 816
and
x
 
factorising 816, we get
816 = 2X 2 X 2 X 2 X 3 X 17
 
Now this is the trickiest part,
 
Here, we have to choose 2 numbers which are les than 50 and 40 respectively, and have product 816.
 
observing closely { or by trial and error method ...:) } ,
 
we can clearly conclude that it is possible for only one pair,
ie. 24 and 34.
 
 
ANS :--  24 and 34.
 
Hope u understood mate...................
 
 
 
 
 
 
 
 
aditya ketkar
40 Points
9 years ago
sorry for the horrible diagram …............... 
i can do nothing for it
 

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