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Question

Three identical square sheets of paper need to be cut into 4, 5, and 6 stripes of equal size respectively. Find the minimum length of the side of the original square sheet.



Your Answer
A

45

Your Answer
B

40

Correct Answer
C

30

Your Answer
D

25


Solution

The correct option is D

30


Since the square sheet needs to be divided equally into 4, 5, and 6 equal parts respectively, its area must be a perfect square divisible by 4, 5, and 6; or the area of the square sheet should be a multiple of 4, 5, and 6.
L. C. M. of 4, 5, and 6 = 60. But 60 is not a perfect square.
60=2×2×3×5=22×3×5.
If we multiply the LCM by 3 and 5 both, it will become a perfect square. Therefore the minimum area of the square sheet =60×3×5=900 sq. units.
Now 900 is a minimum perfect square, which is divisible by 4, 5, and 6. Therefore the side of the square should be the square root of the area of the square (Area of a square = side2 sq. units).
Hence, the minimum length of the side of the square = (900)=(22×32×52) = 30 units.

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