Question

A landscaper has 125 tiles to build a square patio. The patio must have an area of at least 80 square feet.

Answer 1

As given, the number of tiles are = 125

The patio must have area = 80 square feet

Part A.

Assuming the dimensions have to be in exact feet then ,the possible arrangements will be-

As the patio is square, the area is found as = length x length

$9\times9=81 feet^{2}$

$10\times10=100feet^{2}$

or $11\times11=121feet^{2}$

Part B:

For $9\times9=81$ 125-81 = 44 tiles are not used

For $10\times10=100$ 125-100=25 tiles are not used

For $11\times11=121$ 125-121 = 4 tiles are not used.

Answer 2

Given that a square patio of at least 80 square feet is to be built from 125 tiles of length 12 inches or 1 feet.

Part A;
Since there are 125 tiles and the patio has a shape of a square of at least 80 square feet, then the possible dimensions of the patio are

9 ft by 9 ft = 81 ft
10 ft by 10 ft = 100 ft, and
11 ft by 11 ft = 121 ft.


Part B.
For a patio of dimensions, 9ft by 9ft, the number of tiles that will not be used is given by 125 - 81 = 44

For a patio of dimensions, 10ft by 10ft, the number of tiles that will not be used is given by 125 - 100 = 25

For a patio of dimensions, 11ft by 11ft, the number of tiles that will not be used is given by 125 - 121 = 4