Question

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.Find the longest tape which can measure the three dimensions of the room exactly.

Answer 1

Answer:

Length = 825 cm = 3 × 5 × 5 × 11

Breadth = 675 cm = 3 × 3 × 3 × 5 × 5

Height = 450 cm = 2 × 3 × 3 × 5 × 5

Longest tape = HCF of 825, 675, and 450 = 3 × 5 × 5 = 75 cm

Therefore, the longest tape is 75 cm.

Step-by-step explanation:

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Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

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

$\huge ➫ \sf FIND:-$

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

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29$

$925 = 5 \times 5 \times 37$

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

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

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

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

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