Question

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

Answer 1

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

I solve this taking triangle as isosceles triangle..

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