Question

Isabel has a total of eight marbles. She wants to arrange them in rows, each with the same number of marbles. How many different ways she could arrange the marbles to make a perfect rectangle?

• A. $4$
• B. $5$
• C. $3$
• D. $2$

Answer 1

The correct option is A $4$

Total marbles she has: 8
Factors of 6 are 1, 2, 4, 8
Let M denotes a Marble
Case 1: M
M
M
M
M
M
M
M
Total rows = 8
Total Columns = 1
Marbles = Total rows $\times$Total Columns
= 8$\times$1 = 8

Case 2: M M
M M
M M
M M

Total rows = 4
Total Columns = 2
Marbles = Total rows $\times$Total Columns
= 4$\times$2 = 8

Case 3: M M M M
M M M M
Total rows = 2
Total Columns = 4
Marbles = Total rows $\times$Total Columns
= 2$\times$4 = 8

Case 4: M M M M M M M M
Total rows = 1
Total Columns = 8
Marbles = Total rows $\times$Total Columns
= 1$\times$8 = 8