The sides of a rectangular field are in the ratio 4 : 5 and its area is 4500 m². What is the cost of fencing it at Tk. 20 per meter?

Question: The sides of a rectangular field are in the ratio 4 : 5 and its area is 4500 m². What is the cost of fencing it at Tk. 20 per meter?

Solution:
Ratio between the sides of the rectangle = 4 : 5

Let the ratio constant be x.
Then, Length = 5x and Breadth = 4x

According to the question,
4500 = 5x × 4x = 20x²
⇒ x² = 4500 ÷ 20 = 225
⇒ x = 15

Length = 5 × 15 = 75 m
Breadth = 4 × 15 = 60 m

Perimeter = 2 × (Length + Breadth) = 2 × (75 + 60) = 2 × 135 = 270 m

Cost of fencing 1 meter = Tk. 20

Cost of fencing = 270 × 20 = Tk. 5400

∴ Cost of fencing = Tk. 5400.