Question

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

Answer 1

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.

Length = 825 cm, breadth = 675 cm and height = 450 cm

To find the longest tape which can measure the three dimensions of the room exactly, we have to find the H.C.F. of length, breadth and height of the room.

By prime factorisation we get,

03| 825

05| 275

05| 55

11| 11

....| 1

825 = 3 × 5 × 5 × 11

3| 675

3| 225

3| 75

5| 25

5| 5

..| 1

675 = 3 × 3 × 3 × 5 × 5

2| 450

3| 225

3| 75

5| 25

5| 5

..| 1

450 = 2 × 3 × 3 × 5 × 5

Common prime factors = 3, 5 and 5

H.C.F. = 3 × 5 × 5 = 75

Therefore,

75 cm is the longest tape which can measure the three dimensions of the room exactly.

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$</p><p>\tt{\red{Given \: - }}$

$</p><p>\tt{\blue{The \: Length \: Of \: The \: Room \: Is \: 825 \: cm. }}$

$</p><p>\tt{\orange{The \: Breadth \: Of \: The \: Room \: Is \: 675 \: cm. }}$

$</p><p>\tt{\purple{The \: Height \: Of \: The \: Room \: Is \: 450 \: cm. }}$

$</p><p>\tt{\green{Longest \: Tape \: Which \: Can \: Measure \: The \: Three \: Dimensions \: Exactly \: - }}$

$</p><p>\tt{\orange{=> H.C.F \: Of \: The \: Three \: Dimensions }}$

$</p><p>\tt{\purple{</p><p>\begin{array}{r | l}</p><p></p><p>2 & 13860 \\</p><p></p><p>\cline{2-2} 3 & 825 \\</p><p></p><p>\cline{2-2} 5 & 275 \\</p><p></p><p>\cline{2-2} 5 & 55 \\</p><p></p><p>\cline{2-2} 5 & 11\\</p><p></p><p>\cline{2-2} & 1</p><p></p><p>\end{array}}}$

Similarly Factorise The Other Values To Get The HCF.

$</p><p>\tt{\red{=> 75 cm. }}$