In a rectangular Park of dimensions 50 m * 40 m a rectangular pond is constructed so that the area of grass strip of uniform with surrounding the point would be 1184 m square find the length and breadth of the pond.
Answers
See the figure in attachment .
ABCD is the rectangular park .
AB = 50 m
AD = 40 m
Let the length of the strip be x .
The breadth of the inner rectangle = BC - 2 x
BC = AD = 40
Hence breadth = 40 - 2 x
Length = AB - 2 x
= 50 - 2 x
Given that the area of the path is 1184 m² .
Area of path = area of big rectangle - area of small rectangle
⇒ Area of path = ( 40 × 50 ) - ( 50 - 2 x )( 40 - 2 x )
⇒ 1184 = ( 2000 ) - ( 50 - 2 x )( 40 - 2 x )
⇒ 50 ( 40 - 2 x ) - 2 x ( 40 - 2 x ) = 2000 - 1184
⇒ 2000 - 100 x - 80 x + 4 x² = 2000 - 1184
⇒ 4 x² - 180 x + 1184 = 0
⇒ x² - 45 x + 296 = 0
⇒ x² - 37 x - 8 x + 296 = 0
⇒ x ( x - 37 ) - 8 ( x - 37 ) = 0
x = 37
x = 8
x cannot be 37 m because then 50 - 2 x will be negative and side cannot be negative .
So x = 8 m .
Length of the pond = 50 - 2 x
= 50 - 2 × 8
= 50 - 16
= 34
Breadth of pond = 40 - 2 x
= 40 - 2 × 8
= 40 - 16
= 24
Hence the length and breadth of the pond are 34 m and 24 m respectively .
hi mate
here is your answer
refer to the attachment
I have given full explanation in my answer so it is quite long.
hope it helps
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