Question

Choose the following:
Anjelina has a total of six marbles. She wants to arrange them in rows, each with the same number of marbles. What are the different ways she could arrange the marbles to make a perfect rectangle?

• A. Rows = 6, Column = 1
• B. Rows = 2, Column = 4
• C. Rows = 3, Column = 2
• D. Rows = 2, Column = 3
• E. Rows = 1, Column = 6

Answer 1

Answer: (A), (C), (D), (E)

Rows = 1, Column = 6

Total marbles she has: 6
Factors of 6 are 1, 2, 3, 6
Let M denotes a Marble
Case 1: M
M
M
M
M
M
Total rows = 6
Total Columns = 1
Marbles = Total rows $\times$Total Columns
= 6$\times$1 = 6


Case 2: M M
M M
M M
Total rows = 3
Total Columns = 2
Marbles = Total rows $\times$Total Columns
= 3$\times$2 = 6

Case 3: M M M
M M M
Total rows = 2
Total Columns = 3
Marbles = Total rows $\times$Total Columns
= 2$\times$3 = 6

Case 4: M M M M M M
Total rows = 1
Total Columns = 6
Marbles = Total rows $\times$Total Columns
= 1$\times$6 = 6