Question

Michael is an art elective programme student who

is working on an assignment. He plans to cover a
rectangular sheet of paper of dimensions 126 cm by
108 cm with identical square patterns.
(i) What is the least number of square patterns
that could be formed on the sheet of paper?
(ii) How do you determine what other shapes
can the patterns be if they are to fit the sheet of
paper perfectly? Explain your answer.

Answer 1

Explanation:

find the prime factors of given numbers:

126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors

108= 2*2*3*3*3 - same as above

As per prime factors, the squares can be of sizes:

2×2, 3×3, 6×6, 9×9 and 18×18

The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square