a rectangular field is 32 metre wide and 48 metre long. what is the length of the tape by which the length and breadth can be measured exact number of times?
Answers
Given:
(i) A rectangular field is 32 metre wide and 48 metre long.
To find:
(i) The length of the tape which can measure the dimensions exact number of time.
Solution:
The length of the tape which can measure the dimensions of field exact number of times is equal to the LCM of the length and breadth.
32 = 2*2*2*2*2
48 = 2*2*2*2*3
So, LCM = 2*2*2*2*3*2 = 96
Length of tape = 96m
It can measure the length (96/32) = 3 times exactly.
It can measure the breadth (96/48) = 2 times exactly.
So, a 96m of tape can measure the dimensions of the field exact number of times.
Given:
The length of the rectangular field = 48 m
The width of the rectangular field = 32 m
To find:
The length of the tape by which the length and breadth can be measured the exact number of times
Solution:
The length and breadth of the rectangular field have to be measured
the exact number of times by using a tape.
The length of the longest tape by which can measure the rectangular field in exact no. of times will be equal to the H.C.F of the measure of the length and breadth.
Now, we will calculate the H.C.F. by the prime factorization method,
32 = 2 × 2 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3
∴ H.C.F. of 32 and 48 = 2 × 2 × 2 × 2 = 16
Thus, the length of the tape by which the length and breadth can be measured for the exact number of times is 16.
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