The correct answer is option (C):
53m
The problem asks for the length of the longest rod that can be put on the floor of a rectangular room. This means we are looking for the longest distance between any two points on the floor.
Imagine the rectangular room floor as a rectangle. The longest straight line segment that can be drawn within a rectangle is its diagonal. The diagonal connects opposite corners of the rectangle.
We are given the dimensions of the rectangular room:
Length (l) = 45 m
Breadth (b) = 28 m
To find the length of the diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In our case, the length and the breadth of the rectangle form the two shorter sides of a right-angled triangle, and the diagonal of the rectangle is the hypotenuse of this triangle.
Let 'd' be the length of the diagonal. According to the Pythagorean theorem:
d^2 = l^2 + b^2
Substitute the given values of length and breadth into the formula:
d^2 = (45 m)^2 + (28 m)^2
Calculate the squares:
45^2 = 45 * 45 = 2025
28^2 = 28 * 28 = 784
Now, add these values:
d^2 = 2025 + 784
d^2 = 2809
To find the length of the diagonal 'd', we need to take the square root of d^2:
d = sqrt(2809)
Let's calculate the square root of 2809. We can try to estimate or use a calculator.
We know that 50^2 = 2500 and 60^2 = 3600. So, the square root of 2809 is between 50 and 60.
Let's try a number ending in 3 or 7, since 2809 ends in 9.
Try 53: 53 * 53.
53 * 53 = (50 + 3) * (50 + 3) = 50*50 + 50*3 + 3*50 + 3*3 = 2500 + 150 + 150 + 9 = 2500 + 300 + 9 = 2809.
So, the square root of 2809 is 53.
d = 53 m
Therefore, the length of the longest rod that can be put on the floor of the rectangular room is 53 m.
Now let's look at the given options:
A) 45 m (This is the length, not the diagonal)
B) 50 m (This is an approximation, but not the exact value)
C) 53 m (This matches our calculated diagonal)
D) 35 m (This is not related to the dimensions)
E) None of these
Our calculated value of 53 m matches option C.
The final answer is $\boxed{53m}$.