Let the breadth of the rectangular farm be x m.
∴ Length of rectangular farm = (2x + 10) m
Area of rectangular farm = Length × Breadth
= (2x + 10) × x
= (2x2 + 10x) sq. m
Now ,side of square shaped pond = x/3 m
∴ Area of square shaped pond = (side)2
\(=(\frac{x}{3})^2\,m\)
\(=\frac{x^2}{9}\,m\)
According to the given condition,
Area of rectangular farm = 20 × Area of pond
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ x = 0 or x – 45 = 0
x = 0 or x = 45
But, breadth of the rectangular farm cannot be zero,
∴ x = 45
Length of rectangular farm
= 2x + 10 = 2(45) + 10 = 100 m
Side of the pond = x/5 = 45/3 = 15 m
∴ Length and breadth of the farm and the side of the pond are 100 m, 45 m and 15 m respectively.