Question

10 The length, breadth, and height of a room are 7 m 20 cm, 5 m 60 cm, and 4 m,
respectively. What is the largest length of the tape that can be used to measure all
three dimensions, the tape being used an exact number of times in each case?​

Answer 1

Answer:

Length of the room = 7m 20cm

Breadth of the room = 5m 60cm

Height of the room = 4m

To find,

The length of the tape which can measure the three dimensions in exact number of times in each case.

Solution,

First of all, we have to convert the three dimensions into single centimetre unit for easier mathematical calculation.

Length of the room = 7m 20 cm = 700cm + 20cm = 720cm

Breadth of the room = 5m 60cm = 500cm + 60cm = 560cm

Height of the room = 4m = 400cm

[Term of unit conversion = 1m = 100cm]

Now, to find the length of the tape which can measure the three dimensions in exact number of times in each case we have to do the HCF or Highest Common Factor of the three dimensions.

Prime factorization :

720 = 2×2×2×2×3×3×5

560 = 2×2×2×2×5×7

400 = 2×2×2×2×5×5

HCF = 2×2×2×2×5 = 80

Hence, the length of the tape will be 80cm.