Question

In the Centre of a rectangular lawn of dimensions 50m X 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m 2 . Find the length and breadth of the point.

Answer 1

Solution:-
L = 50 m and B = 40 m
Area of the rectangular lawn = 50*40 
= 2000 sq m
Area of the grass surrounding the pond = 1184 sq m
Then, the area of the pond = Area of the rectangular lawn - Area of the grass surrounding the pond 
= 2000 - 1184 
= 816 sq m
Let the width of the grass be 'x' meter.
Then length of rectangular pond = 50 - 2x
and breadth of the rectangular pond = 40 - 2x
Now, according to the question.
⇒ (50 - 2x)(40 - 2x) = 816
⇒ 4x² - 180x + 2000 = 816
⇒ 4x² - 180x + 2000 - 816 = 0
⇒ 4x² - 180x + 1184 = 0  (Dividing it by 4, we get)
⇒ x² - 45x + 296 = 0
⇒ x² - 37x - 8x + 296 = 0
⇒ x(x - 37) - 8(x - 37) = 0
⇒ (x - 37) (x - 8) = 0
⇒ x = 37 or x = 8
x = 37 is not possible because if we take x = 37, the length and breadth will be in negative, which is not possible.
{50 - (2*37)}
= 50 - 74 
= - 24 length cannot be negative.
So, x = 8 is the correct value.
Length of the rectangular pond
= 50 - 2*8
= 50 - 16 
= 34 m
and,
Breadth of the rectangular pond 
= 40 - 2*8
= 40 - 16
= 24 m
So, L = 34 and B = 24 m
Answer.