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How many rectangular tiles \[10\] cm by \[7\] cm will be required to cover the floor \[14\] m by \[12\dfrac{1}{2}\] m and what will be the cost at Rs. \[5\] per hundred tiles?

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Last updated date: 14th Jul 2024
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Answer
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Hint: In a given problem it is clearly mentioned that the tiles are in the shape of rectangle so we can solve the given problem by using the formula of area of rectangle and is given by \[{{Area = length \times breadth}}\] .once the area is obtained then we can find the cost of the tiles.

Complete step-by-step answer:
Given: dimensions of rectangular tiles are
Length \[ = 10cm\]
Breadth \[ = 7cm\]
Therefore, the area of rectangular tiles \[{{ = length \times breadth}}\]
 \[ = 10 \times 7\]
the area of rectangular tiles \[ = 70c{m^2}\]
Dimensions of the floor are
Length \[ = 14m\]
Breadth \[ = 12\dfrac{1}{2}m = \dfrac{{25}}{2}m\]
Since the length of tiles is given in terms of centimeters but the length and breadth of the floor is given in terms of meters so we have to convert the length and breadth of the floor from meters to centimeters by multiplying it with 100 then the new length and breadth of the floor is given by
Length \[ = 14 \times 100 = 1400cm\]
Breadth \[ = \dfrac{{25}}{2} \times 100m = 1250cm\]
Therefore, the area of rectangular floor \[{{ = length \times breadth}}\]
 \[ = 1400 \times 1250\]
the area of rectangular floor \[ = 1750000c{m^2}\]
Therefore, the total number of tiles required \[ = \dfrac{{area{\text{ }}of{\text{ }}floor}}{{area{\text{ }}of{\text{ }}tile}}\]
Substituting the area calculated above we get,
the total number of tiles required \[ = \dfrac{{1750000}}{{70}}\]
on simplification, the total number of tiles required \[ = 25000\]
now cost can be calculated as \[{{cost = tiles \times rate}}\]
 \[ = 25000 \times \dfrac{5}{{100}}\]
cost \[ = 1250\] Rs

Note: After calculating the area of rectangle the unit for area depends on the units of dimensions given for example in the above problem both length and breadth are given in terms of centimeters so unit for area should be taken as \[c{m^2}\] .if the length and breadth is given in terms of meter then unit for area should be taken as \[{m^2}\] .