Word problem

Question

Mr. Fair has ordered new chairs for the school gym. He ordered a total of 84 chairs for family and guests to sit in. If he arranges the chairs in one large square, how many chairs will not fit into the square? Explain your answer.

Answer 1

A square arrangement has the same number of rows and chairs in a row, e.g. six rows of six chairs.

What is the largest perfect square less than 84?

 

 

Answer 2

Hello Toby,

The fewest chairs you would need to form a square would be 4 -- that is, 2 by 2, or 2 squared, that is 2². The next amount of chairs would be 9, or 3². The first nine perfect squares are then 4, 9, 16, 25, 36, 49, 64, 81, 100.  If you have 84 chairs, you'll have 3 extra chairs that won't fit into the square of 9 by 9, or 9² = 81 chairs.

 

Hope this Helps.

John B.

Answer 3

To form a square we need to have the same number of

chairs across each row as the number of rows

 

10 by 10 would take 100 chairs so too many:   10²=100

8 by 8 would take 64:     8² = 64

 

9 rows of 9 chairs each would be 81 chairs:  9² = 81
This leaves 3 chairs out.