Question

A rectangular courtyard is18 m 72 cm and 13 m 20 cm broad It is to be paved with sqare tiles of the same size. Find t
he least possible number if such tiles

Answer 1

Solutions :-

Given :
Length of rectangular courtyard = 18 m 72 cm = 1872 cm
Breadth = 13 m 20 cm = 1320 cm


Find the area of rectangular courtyard :-

Area of rectangle = (Length × Breadth) sq. units
= (1872 × 1320) cm²
= 2471040 cm²


Now,
Find the HCF of 1872 and 1320 :-

The prime factors of 1872 and 1320 are :-

1872 = 2⁴ x 3² x 13

1320 = 2³ x 3 x 5 x 11

HCF of 1872 and 1320 = 2³ x 3 = 24


Find the least possible number of such tiles :-

= Area of rectangular courtyard / Area of square tiles
= 2471040/(24)²
= 2471040/576
= 4290


Hence,
The least possible number of such tiles = 4290

Answer 2

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

Dear ,

Your Answer is ; 4290 tiles

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• Step by Step Explanation ;-
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Given that ;-
• Rectangular Courtyard's lenght = 18 m and 72 cm. i.e. = 1872 cm.
• Breadth = 13 m and 20 cm i.e. = 1320 cm.

Now ,
Finding the area of Rectangular Courtyard ;-

We know that ;-

Area of Rectangle = Lenght × Breadth

So ,

$= > (1872 \times 1320)cm^{2}$
$= > 2471040 \: cm^{2}$
Now , Finding the Highest Common Factor of 1872 and 1320 ;-

$= > 1872 = 2^{4} \times {3}^{2} \times 13$
$and \: = > 1320 = 2^{3} \times 3 \times 5 \times 11$
Hence , HCF of 1872 and 1320 is = 24.

Now ,
Finding the least possible numbers of given tiles ;-

$= > \frac{24710040}{24^{2} } = 4290$
Therefore ,
4290 is the least possible number of such tiles.


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