The perimeter of a square is equal to the perimeter of rectangle. The length of the rectangle is three times longer than its width having total area of 1,200 sq meters. What will be the total cost if the total area of the square is covered is covered with stones having a dimension of 50 centimeter square each and if Tk. 50 is charged for placing as stone in the square? (পরিমিতি)

Let, width of the rectangle be x meter

Length of the rectangle be 3x meter

According to question, 

$$\begin{gathered} 3x\times x=1,200 \\ \Rightarrow 3x^2=1,200 \\ \Rightarrow x^2= \frac{1,200}{3} \\ {x}^2=400 \\ \therefore x= \sqrt{400} \\ x=\sqrt{{\left(20\right)}^2} \\ x=20 \end{gathered}$$

The perimeter of rectangle will be $2\left[\left(3\times 20\right)+20\right]=2\left(60+20\right)=2\times 80=160$ meter

Perimeter of the square, 4a=160 

One side of the square will be 40 meter

Area of the square will be = (40 x 40) = 1,600m² 

Now, length of 1 stone is 50cm = $\frac{50}{100}=0.5 m$ 

Area of one stone will be =$(0.5x0.5)=0.25 m²$

Number of stone required to cover the square = 1,600+0.25=6,400 pieces

Total amount of taka required at 50 tk per stone is $6,400 \times 50 = 3,20,000$ Tk. ans.