PLEASE ANSWER THIS QUESTION.
Answers
S O L U T I O N :
Given :- A rectangular courtyard is 20m 16cm long and 15m 60cm broad.
[ First convert m into cm. ]
⟹ Length = 20 × 100 + 16
⟹ Length = 2016 cm
⟹ Breath = 15 × 100 + 60
⟹ Breadth = 1560 cm
We know that,
Area of courtyard = Length × Breath
⟹ Area of courtyard = 2016 × 1560
⟹ Area of courtyard = 3144960 cm²
Now, take HCF of (2016 , 1560),
⟹ 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
⟹ 1560 = 2 × 2 × 2 × 3 × 5 × 13
⟹ (2016 , 1560) = 2 × 2 × 2 × 3
⟹ (2016 , 1560) = 24
.°. Side of square stone is 24 cm.
Area of square stone = (Side)²
⟹ Area of square Stone = (24)²
⟹ Area of square Stone = 576 cm²
Let number of stones be "R".
Now,
Number of stones = Area of rectangular courtyard / Area of square stone
[ Put the values ]
⟹ R = 3144960 / 576
⟹ R = 5460
Therefore,
The number of stones is 5460.
Question :-
A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of stones.
Answer :-
No. of stones = 5460
Given :-
↬Length = 20m 16cm
↬Width = 15m 60cm
To Find :-
↬ No. of stones ?
Solution :-
So , as per the given the courtyard is in rectangular shape . Therefore ,
The area of rectangle = Area of courtyard
↬ Area = Length × Breadth
Converting the length and breadth in cm first .
↬ New length = 20 × 100 + 16 = 2016 cm
↬ New Breadth = 15 × 100 + 60 = 1560 cm
According to the Question , Now :-
= 2016 × 1560
↬ Area is 3144960 cm²
In order to find the side of stone first lets take HCF {2016 , 1560}
The required factors :-
↬ 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
↬ 1560 = 2 × 2 × 2 × 3 × 5 × 13
Therefore the required H.C.F :-
↬ 2 × 2 × 2 × 3
↬ = 24
We get side of stone = 24 cm.
Now , simply finding the area of stone
From given we know that it is in square shape .
So , Area of Square = Area of square stone = (Side)²
↬ (24)²
= 576 cm²
Now , Finding the no. of stones :-
No. of stones =
Substituting the values in the above formula :-
↬ No. of stones = 3144960 / 576
↬ Number of stones = 5460