Question

The length, breadth and height of a room are 6 m 50 cm, 3 m 50 cm and
longest tape which can measure the three dimensions of the room exactly
o room are 6 m 50 cm. 3 m 50 cm and 3 m. determine the longest tape which can measure the three dimensions of the room exactly .


Please solve it.​

Answer 1

as length of the room is the greatest so length of time should be exactly same to it so it can measure all three dimensions

so length of tape should be 6m 50cm

Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

$length \: of \: room \: = 7m25cm = 725cm \\ breadth \: of \: room \: = 9m25cm = 925cm \\ height \: of \: room \: = 8m25cm = 825cm$

$\huge ➫ \sf FIND:-$

$now \: we \: find \: HCF \: of \: 725,925 \: and \: 825$

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29 \\ 925 = 5 \times 5 \times 37 \\ 825 = 3 \times 5 \times 5 \times 11 \\ \\ so, \: heighest \: common \: factor \: is \: 5 \times 5 = 25 \\ therefore \: HCF \: of \: 725,925,825 \: is \: 25. \\ \therefore 25m is \: the \: longest \: tape \: measure \: which \: can \: measure \: all \: the \: dimensions.$

$so, \: answer \: is \: \boxed{ \mathfrak{ 25m}}$