A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.

For rectangular park

Let the breadth of park = b

Length of park = b + 3 (as breadth is 3 m less than length)

For triangular park

Base = breadth of park = b

Altitude = 12 m

Now Given that

Area of rectangular park = 4 m² + area of triangular

b² + 3b - 4 = 6b

b² - 3b - 4 = 0

b² - 4b + b - 4 = 0

(b - 4)(b + 1) = 0

b = 4 or b = - 1

as b = - 1 is not possible as breadth of park is not negative.

Length = b + 3 = 3 + 4 = 7 m

Breadth = b = 4 m