question_answer 1)

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm, respectively. Find the longest tape, which can measure the three dimensions of the room exactly.

Answer:

                For the longest tape, which can measure dimensions of room exactly, we have to find out the HCF of dimensions, i.e. 3 825 3 675 2 450 5 275 3 225 3 225 5 55 3 75 3 75 11 11 5 25 5 25 1 5 5 5 5 1 1 \[\therefore \] Prime factorisation of \[825=\times \times \times 11\] Prime factorisation of      \[675=\times \times \times 3\times 3\] Prime factorisation of      \[450=\times \times \times 3\times 2\] \[\therefore \] Common factors of 825, 675 and 450 are 3 and 5 (occurring twice). Thus, HCF of 825, 675 and \[450=3\times 5\times 5=75\] Hence, required measure of longest tape = 75 cm