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.

• A. 45
• B. 40
• C. 30
• D. 25

Answer 1

The correct option is C

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.
$60=2\times 2\times 3\times 5=2^2\times 3\times 5$.
If we multiply the LCM by 3 and 5 both, it will become a perfect square. Therefore the minimum area of the square sheet $=60\times 3\times 5=900$ 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 = $sid{e}^2$ sq. units).
Hence, the minimum length of the side of the square = $\sqrt{\left(900\right)}=\sqrt{(2^2\times 3^2\times 5^2)}$ = 30 units.