A rectangular park is to be designed whose breadth is 3 m less than its length

• Quadratic Equations (C10)

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 its length and breadth.

Solution

Let the breadth of the rectangular park be x m.

So, its length = (x + 3) m.

Therefore, the area of the rectangular park = x(x + 3) m² = (x² + 3x) m².

Now, base of the isosceles triangle = x m.

Therefore, its area = ½ × x × 12 = 6x m².

According to the question,

x² + 3x = 6x + 4

x² – 3x – 4 = 0

Using the quadratic formula,

x = 4 or –1

But x ≠ – 1. Therefore, x = 4.

So, the breadth of the park = 4 m and its length will be 7 m.

Verification:

Area of rectangular park = 28 m²

Area of triangular park = 24 m² = (28 – 4) m²