Question

Mr Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs. 55 per sq. metre.

Answer 1

Hint: We will first find the area of the plot by using the formula $s \times s$, where $s$ is the length of the side of the square. Next, find the area of the house by using the formula $l \times b$, where $l$ is the length of the house and $b$ is the breadth of the house. Then, find the area of the garden by subtracting the area of the house from the area of the square plot. To find the total cost, multiply the area of the garden with a rate of 1 sq. metre.

Complete step by step solution: We are given that the house is in the middle of the plot.
We have to find the cost of developing a garden around the house.
We will first find the area of the garden.
The plot is in square shape and the house is of rectangular shape. Label the points of the given figure.

We will first calculate the area of the whole plot, that is the area of the square PQRS
Here, we can see that the side of the square is 25m.
And we know that the area of the square is $s \times s$, where $s$ is the length of the side of the square.
On substituting the value of side, we get the area of plot as,
$25 \times 25 = 625{m^2}$
Now, we calculate the area of the house.
We can see that the length of the house is 20m and the breadth of the house is 15m.
Also, ABCD is a rectangle.
The area of the rectangle is the product of its length and breadth.
Hence, the area of the house is $20 \times 15 = 300{m^2}$
To find the area of the garden, we will subtract the area of the house from the area of the plot.
Therefore, the area of the garden is $625 - 300 = 325{m^2}$
Now, we are given that the rate of developing a garden is Rs. 55 per sq. metre.
We will multiply the area of the garden with a rate of 1 sq. metre to find the total cost.

Hence, total cost of developing a garden around the house is $325 \times 55 = {\text{Rs}}.17,875$.

Note: Many students make mistakes by finding the perimeter of the garden and then multiplying it with the given rate, which is incorrect. We use perimeter only when we have to find the length of the boundary. Also, the area is always measured in square units.