Question

Huixan wishes to cut some squares from a rectangular sheet of A4 paper with a length of 126 cm and a breadth of 84 cm.She wants to cut the A4 paper evenly into small squares and does not want any leftover paper .

What is the length of each square and how many square can she cut together

Answer 1

Huixan can cut six 42x42 cm squares from the A4 paper, as 42 cm is the greatest common divisor of the paper's length and breadth (126 cm and 84 cm, respectively).

Step-by-step explanation:

Huixan wants to cut a rectangular A4 paper evenly into small squares without any leftover paper. To do this, she must determine the largest square size that can evenly divide both the length and the breadth of the A4 paper. The length of the A4 paper is given as 126 cm, and the breadth is 84 cm. The largest square size will correspond to the greatest common divisor (GCD) of these two dimensions.

By performing the Euclidean algorithm or using a GCD calculator, we find that the GCD of 126 and 84 is 42. Therefore, the length of each square that Huixan can cut from the A4 paper is 42 cm. To find how many such squares she can cut, we will divide the length and breadth of the A4 paper by the side of the square and then multiply the two results. That is (126 cm / 42 cm) × (84 cm / 42 cm) = 3 × 2 = 6 squares in total.

So, Huixan can cut six 42x42 cm squares from the A4 paper.