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?

Question

Mathematics

Kaeden Deleon

5 January, 18:59

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?

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Ortiz · 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