The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm, and 4m 75 cm respectively. What will be the length of the longest rod that can measure the dimensions of the room exactly?

To find the length of the longest rod that can measure the dimensions of the room exactly, we need to find the greatest common divisor (GCD) of the dimensions.

Step 1: Convert all measurements to the same unit. In this case, we'll convert meters to centimeters because the measurements are given in a mix of meters and centimeters.

1 meter = 100 centimeters

So, the dimensions of the room in centimeters are:

Length = 8 m 50 cm = 850 cm Breadth = 6 m 25 cm = 625 cm Height = 4 m 75 cm = 475 cm

Step 2: Find the GCD of the three dimensions.

The GCD of 850 cm, 625 cm, and 475 cm is 25 cm.

So, the length of the longest rod that can measure the dimensions of the room exactly is 25 cm.