What is the cost of tiling a rectangular plot of land 500m long and 200m wide at the rate of ₹ 8 per hundred sq m?

Text Solution

Solution : 'The length is given as 500 m and breadth is given as 200 m hence, the area can be calculated using the given formula. Area of rectangular plot = length × breadth Area of rectangular plot = 500 × 200 = 1,00,000 `m^2` Now, the cost of tilling the rectangular plot per hundred sq m. = ₹8 So, the cost of tiling 1,00,000 sq m. of land = (8/100) × 1,00,000 = ₹ 8000`m^2` Therefore, the cost of tiling 1,00,000 sq m. of land is ₹ 8000 `m^2` '

Answer

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Hint: In this question, we need to determine the cost of tiling a rectangular plot of land 500 meters long and 200 meters wide at the rate of Rs.8 per hundred square meters. For this, we will first evaluate the area of the plot and then, multiply the result with 8 to get the final result.

Complete step-by-step answer:

The product of the length and the width of the rectangle results in the area of the rectangle. Mathematically, $ A = lb $ where, ‘l’ is the length of the rectangle and ‘b’ is the width of the rectangle.

Here, the dimension of the rectangular plot has been given as 500 meters long and 200 meters wide. So, substitute ‘l=500 meters’ and ‘b=200 meters’ in the formula $ A = lb $ to determine the area of the rectangular plot. $ \Rightarrow A = lb \\ = 500 \times 200 \\ = 100000{\text{ }}{{\text{m}}^2} \\ = {10^5}{\text{ }}{{\text{m}}^2} \\ $ Hence, the area of the rectangular plot is $ {10^5}{\text{ }}{{\text{m}}^2} $ . Now, according to the question, the rate of tiling the rectangular plot is Rs.8 per hundred square meters, i.e., for tiling 100 square meters of the plot it will cost Rs.8. So, by using the unitary method to determine the total cost of tiling, the rectangular plot of land is: $ 100{\text{ }}{{\text{m}}^2} = Rs.8 \\ 1{\text{ }}{{\text{m}}^2} = Rs.\left( {\dfrac{8}{{100}}} \right) \\ {10^5}{\text{ }}{{\text{m}}^2} = Rs.\left( {\dfrac{8}{{100}}} \right) \times {10^5} \\ = Rs.8,000 \\ = Rs.8000 $ Hence, the total cost of tiling the rectangular plot of dimension (500 m x 200 m) is Rs.8000.

Note: As the tiles are located on the floor only so, we have evaluated the area of the base of the rectangular plot of land only. However, if in the question, it is mentioned that the tiles are located at any other positions then, we have to evaluate the area of that region and then, multiply it with the cost.