The sides of a rectangular park are in the ratio 4:3. If the area is1728 m², find the cost of fencing it at the rate of Rs. 2.50/m.

Let us consider a Rectangle ABCD,

According to the problem, it is given that

The sides are in the ratio 4:3.

The area of Rectangle is 1728m².

The cost of fencing is Rs.2.50/m.

Let us consider the length(L) of the Rectangle be ‘4x’m and the breadth(B) of the rectangle be ‘3x’m.

We know that Area(A) of a Rectangle is

A = L × B

From the given data we can write,

⇒ 4x × 3x = 1728

⇒ 12x² = 1728

⇒

⇒ x² = 144

⇒ x = √144

⇒ x = 12

Now we find the length and breadth of the triangle.

⇒ Length(L) = 4x

⇒ L = 4 × 12

⇒ L = 48m

⇒ Breadth(B) = 3x

⇒ B = 3 × 12

⇒ B = 36m

To find the total cost for fencing, we need to find the perimeter first.

As we know that the fencing the sides of the rectangle but not total internal part of the rectangle.

Now, let’s find the Perimeter (P) of the rectangle.

We know that Perimeter(P) of the Rectangle is

P = 2 × (L + B)m

Now let’s substitute the values of length and breadth of the rectangle.

⇒ P = 2 × (48 + 36)

⇒ P = 2 × (84)

⇒ P = 168m

The total cost required for fencing(F_c) = Perimeter*cost per meter

⇒ F_c = 168 × 2.50

⇒ F_c = 420

The total fencing cost required is Rs.420.