Question

What is the length of the longest rod that can be put on the floor of a rectangular room measuring 45 min length and 28 m in breadth?

• A. 45 m
• B. 50 m
• C. 53m
• D. 35m
• E. None of these

Answer 1

The Correct Option is C

Step 1: Understand the problem.
We are asked to find the length of the longest rod that can be placed on the floor of a rectangular room. The length and breadth of the room are given as 45 meters and 28 meters, respectively. The longest rod that can be placed in the room will be the diagonal of the rectangle.

Step 2: Use the Pythagorean Theorem.
The longest rod will form the hypotenuse of a right-angled triangle, where the length and breadth of the room are the two perpendicular sides. According to the Pythagorean theorem, the diagonal (hypotenuse) \( d \) can be found using the formula:
\( d = \sqrt{l^2 + b^2} \)
where \( l \) is the length and \( b \) is the breadth of the room.
Substituting the values \( l = 45 \, \text{m} \) and \( b = 28 \, \text{m} \):
\( d = \sqrt{45^2 + 28^2} \)
\( d = \sqrt{2025 + 784} \)
\( d = \sqrt{2809} \)
\( d = 53 \, \text{m} \)

Step 3: Conclusion.
The length of the longest rod that can be placed in the room is 53 meters.

Final Answer:
The length of the longest rod that can be placed on the floor is 53 meters.