Question

the Length breadth and height of a room are 1050 CM 750 cm and 425 CM respectively find the length of the longest tape which can measure the three dimensions of the room exactly

Answer 1

longest tape=√(l2+h2+b2)
=1358.5 cm

Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

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

$\huge ➫ \sf FIND:-$

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

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29$

$925 = 5 \times 5 \times 37$

$825 = 3 \times 5 \times 5 \times 11$

$so, \: heighest \: common \: factor \: is \: 5 \times 5 = 25$

$therefore \: HCF \: of \: 725,925,825 \: is \: 25.$

$\therefore 25m is \: the \: longest \: tape \: measure \: which \: can \: measure \: all \: the \: dimensions.$

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