Question

The floor of an auditorium is in the shape of a rectangle around which vertical walls are raised. If the perimeter of a floor is $110$mts and the height of the auditorium is $15$ mts then the cost of painting the four walls at the rate of Rs.$720$ per 100sq.mts is

Answer 1

Hint: Given the perimeter of a floor is $110$mts.
Therefore using the perimeter formula we can find the length and breadth of the floor. Using this we will find the area of four walls.
We are asked to find the cost of painting four walls, so using the area of four walls we can determine the cost of painting four walls at the rate of Rs. $720$per $100$sq.mts.

Complete step-by-step solution:

Given that the perimeter of a floor is $110$mts. Since the auditorium is in the shape of a rectangle, we are going to use the perimeter of a rectangle formula,
i.e., Perimeter of a rectangle = $2$(l + b)
The perimeter of a floor = $110$
2 (l + b) = $110$
Giving 2 to another side, we get
l + b = $\dfrac{{110}}{2}$
Therefore, l + b = $55$
Now, we have to find the area of four walls using the values of (l + b), We know that,
Area of two walls = $2$lh
Area of two walls = $2$bh
Therefore,
Area of four walls = $2$lh + $2$bh
Since $2$ and h are common on both terms, we can take it outside. We get,
Area of four walls = $2 \times $h (b + l)
We have found that the value of b + l is $55$, using this in the above formula, we get
Area of four walls = $2 \times $h $ \times $$55$
From the question, it is given that the height of the wall is 15mts, substituting the value of h, we get
Area of four walls = $2 \times $$15$$ \times $$55$
= $1650$
Given that,
Cost of painting for $100$sq.mt = Rs. $720$
Therefore, for $1$ sq.mt = Rs. $\dfrac{{720}}{{100}}$
We have to find the cost of painting the four walls, i.e, the area of four walls
Therefore, for 1650 sq.mt = Rs. $\dfrac{{720}}{{100}} \times 1650$
= Rs. $72 \times 165$
 = Rs. $11,880$
Hence, the cost of painting the four walls at the rate of Rs.$720$per $100$sq.mt is Rs. $11,880$

Note: If the floor is in any other shape other than rectangle we have to use different formulae according to the shape of the floor. The area of walls also changes according to the shape. For any other shapes, we will be using different formulae. Before finding the cost of painting we have to convert the cost Rs.$720$ per $100$sq.mt into per sq.mt.