Question

(a) The length, breadth and height of a room is 32m, 24m, and 20m respectively.
What is the greatest length of the tape that can be used to measure all these dimensions,
the tape being used as exact number of lines in each case?​

Answer 1

Answer:

The length, breath and height of a room are 8m 25cm, 6m 75cm and 4 m 50cm respectively. Find the longest tape, which can measure the three dimensions of the room exactly.

Length of the room = 8m 25cm = 825 cm

Breadth of the room = 6m 75cm = 675 cm

Height of the room = 4m 50cm = 450 cm

Prime factorization of 825, 675 and 450 are as follows:

825 = 3×5×5×11

675 = 3×3×3×5×5

450 = 2×3×3×5×5

Common factors = 3×5×5

H.C.F. = 75

Hence, H.C.F. of 825, 675 and 450 is 75.

Therefore the length of the longest tap is 75 cm which can measure the three dimensions of the room exactly.

Answer 2

Answer:

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