Question

Determine the longest tape which can be used to measure exactly the length 7m, 3m
85cm & 12m 95cm

Answer 1

First change the length into cm.

[1m= 100cm]

7m= 700cm
3m 85cm= 3×100+85= 385cm
12m95cm= 12×100+95=1295cm

Find the H.C.F of 3 lengths 700cm, 385cm, 1295cm

700= 2× 2× 5×5×7 = 2²×5²×7
385= 5×7×11
1295= 5×7×37

H.C.F= 5×7 = 35
_____________________________
The longest tape which can be used to measure exactly the length 700cm, 385cm & 1295cm = 35
_____________________________
Hope this will help you..

Answer 2

Solution :-

To find the length of the longest tape to be used for measuring the 7 m, 4 m 85 cm and 12 m 95 cm exactly, we have to find the H.C.F. of these lengths.

7 m = 700 cm

3 m 85 cm = 385 cm

12 m 95 cm = 1295 cm

H.C.F. of 700, 385 and 1295

        ________________ 
     5 | 700, 385, 1295
        |_____________
     7 | 140, 77, 259 
        |_____________
        |  20, 11,  37 
        |
        
H.C.F. of 700, 385 and 1295 = 5*7 = 35

= 35 cm

The length of the longest tape is 35 cm which can be used to measure exactly the length 7 m, 3 m 85 cm and 12 m 95 cm.
 
Answer.