A square is divided into certain number of equal parts. If 22 such equal parts represent 1/15 of the square then the total number of equal parts of the square is..................... .
option:-
A. 300
B. 250
C. 330
D. 200
Answers
The square is divided into 22 equal parts .
Let the side of the square be a .
Then area of a square = length × area of cross section
= a × a [ area of cross section = side of square ]
= a²............................(1)
They are divided into say n equal parts .
Area = a² is divided into n parts
Then the area of each part is a²/ n......................(2)
Given 22 equal parts has an area equal to 1/15 th of the square.
Area of 22 equal parts = area of each part × 22
= a²/n × 22 [ From (1) ]
= 22 a² / n ....................(3)
Area of 1/15 th of the square is = area of square / 15
= a² / 15 [ From (2) ] ......................(4)
(3) is equal to (4) as per the question .
So this leads us to : 22 a²/n = a² / 15
[Dividing both sides by a²]
==> 22 / n = 1 / 15
==> n = 22×15
==> n = 330.
Sorry for making the answer long and boring.
The number of parts is 330.
Right answer is : OPTION ( C )
Hope it helps you :-)
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Answer:
Option(C)
Step-by-step explanation:
Let the total number of equal parts be 'x'.
Given that 22 such parts = (1/15) of the square.
Then, x such parts = 1.
Here, ratio of the first two quantities is equal to the ratio of last two.So, they are in proportion.
According to the given condition,
= 22 : 1/15 :: x : 1
Product of extremes = Product of means.{ad = bc}
22 * 1 = x/15
22 = x/15
330 = x.
Therefore, the total number of equal parts of the square is 330.
Hope it helps!