Question

A rectangular courtyard is 21m 36cm long and 17m 4cm broad. It is to be furnished with square stones of the same size. Find the least possible number of such stones.​

Answer 1

❍ Given : A rectangular courtyard is 21m 36cm long and 17m 4cm broad is to be furnished with square stones of the same size.

❍ To find : The least possible number of such stones.

$\qquad$_______________

☀ Converting the dimensions of the rectangular courtyard into cm :

$~$

$\sf \bigstar~ Length~:~21m~36cm$

$\sf \qquad \dashrightarrow \: 2100 cm+ 36m$

$\sf \qquad \dashrightarrow \:2136cm$

$~$

$\sf\bigstar~ Breadth~:~17m~ 4cm$

$\sf \qquad \dashrightarrow \: 1700cm + 4cm$

$\sf \qquad \dashrightarrow \: 1704cm$

$~$

❏ So, the dimensions of the rectangular field are 2136cm and 1704cm.

$\qquad$______________

☀ Finding the HCF of the dimensions of the rectangular field's dimensions to know the dimensions of the square stones using Euclid's division lemma as the edge of the square tile should be the highest divisor dividing the dimensions of the field :

$~$

$\sf \bigstar~ a=bq+r$

$\sf \qquad \dashrightarrow \: 2136 = 1704 \times 1 + 432$

$\sf \qquad \dashrightarrow \: 1704 = 432 \times 3 + 408$

$\sf \qquad \dashrightarrow \: 432 = 408 \times 1 + 24$

$\sf \qquad \dashrightarrow \: 408 = 24 \times 17 + 0$

$~$

❏ Therefore, 24 is the HCF of 2136 and 1704.

❏ Henceforth, the maximum edge of the square stone is 24cm.

$\qquad$______________

☀ Finding the areas of the rectangular field and the square stone :

$~$

$\sf\bigstar~Area_{(rectangle)}=lb$

$~$

$\sf \qquad \dashrightarrow \: 2136cm ~(~1704cm ~)$

$\sf \qquad \dashrightarrow \: 3639744 \: {cm}^{2}$

$\sf\bigstar~Area_{(square)}=s^2$

$\sf \qquad \dashrightarrow \: (~ 24cm~)^{2}$

$\sf \qquad \dashrightarrow \: 576 \: {cm}^{2}$

$~$

❏ Therefore, the area of the rectangular field is 3639744 cm² and the area of the square stone is 576cm².

$\qquad$______________

☀ Finding the number of square stones required :

$~$

$\sf\bigstar~ No.~of~ square~ stones~ required ~=~ \dfrac{Area_{(rectangle)}}{Area_{(square)}}$

$\sf \qquad \dashrightarrow \: \dfrac{3639744 \: cm ^{2} }{576 \: cm ^{2} }$

$\sf \qquad \dashrightarrow \: \cancel{\dfrac{151656}{24} }$

$\sf \qquad \dashrightarrow \: 6319 \: stones$

$~$

❏ Therefore, 6319 stones are required for the rectangular field.

Answer 2

Step-by-step explanation:

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