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 dimens

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.

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Nevaeh 2 weeks 2021-09-12T16:53:04+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-12T16:54:31+00:00

    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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    0
    2021-09-12T16:54:57+00:00

    ➪ \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}}

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