Question

The length, breadth and height of a room are 658 cm, 940 cm and 1128 cm respectively. Find the length of the longest tape which can measure the three dimensions of the room exactly.

Answer 1

the longest tape is the diagonal of the room

diagonal of cuboid = √Length^{2} + Breadth^{2}  + Height^{2}

                               = √ 658^{2} + 940^{2}  + 1128^{2}

                              = √432964 + 883600 + 1272384

                              = √2588948

                              = 1609.02 cm³

Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

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

$\huge ➫ \sf FIND:-$

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

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29$

$925 = 5 \times 5 \times 37$

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

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

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

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

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