Question

a landscaper has 125 tiles it has to be a square patio , the patio has to have at least an area of 80 square feet what are the possible arrangements? And how many tiles are not used in the arrangements?

Answer 1

Area of a square is given by multiplying the length by the width, but since a square has four sides of equal length, we will end up multiplying two numbers that are the same.

We want a minimum area of 80 square feet and at the maximum of 125 square feet

Think of the square numbers that are in between 80 and 125

8 × 8 = 64
9 × 9 = 81
10 × 10 = 100
11 × 11 = 121
12 × 12 = 144

There are three possible measurements of the patio:

9 by 9 and number of tiles left = 125 - 81 = 44 tiles
10 by 10 and number of tiles left = 125 - 100 = 25 tiles
11 by 11 and number of tiles left = 125 - 121 = 4 tiles