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Question

A Mansion has to fit a bathroom with square marble tiles of the largest possible size the size of the bathroom is 10 feet by 8 feet what would be the size in inches of The tile required that has to be cut and how many such tiles are required

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Solution

Size of Bathroom = 10 feet by 8

We know that 1feet = 12 inches

So, 10 feet = 10 X 12 => 120 inches

8 feet = 8 X 12 => 96 inches

Now, We will find the HCF of ( 120,96 ) to find the side of a square tile

By prime factorization method :-

120= 2^3 X 3 X 5

96 = 25 X 3

So, HCF ( 120 , 96 ) = 2^3 X 3 = 24 inch

Now, We will find the number of square tiles:-

Number of Square tiles = Area of Bathroom / Area of Square Tiles

= Length X Breadth / side^2

= 120 X 96 / 24 X 24

= 11520 / 576

= 20 tiles ANS

Alternate solution

find GCD of 10 and 8

It is 2.

1ft=12in, so 2ft=24in.

24 is the size (in inches),

To see how many are required,

8ft/24in

=8ft/2ft

=4

10ft/24in

10ft/2ft

=5

4×5=20

ANS: 20tiles of 24in side length.

We know that 1feet = 12 inches

So, 10 feet = 10 X 12 => 120 inches

8 feet = 8 X 12 => 96 inches

Now, We will find the HCF of ( 120,96 ) to find the side of a square tile

By prime factorization method :-

120= 2^3 X 3 X 5

96 = 25 X 3

So, HCF ( 120 , 96 ) = 2^3 X 3 = 24 inch

Now, We will find the number of square tiles:-

Number of Square tiles = Area of Bathroom / Area of Square Tiles

= Length X Breadth / side^2

= 120 X 96 / 24 X 24

= 11520 / 576

= 20 tiles ANS

Alternate solution

find GCD of 10 and 8

It is 2.

1ft=12in, so 2ft=24in.

24 is the size (in inches),

To see how many are required,

8ft/24in

=8ft/2ft

=4

10ft/24in

10ft/2ft

=5

4×5=20

ANS: 20tiles of 24in side length.

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