Question

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

A. What are the possible arrangements for this patio?
B. How many times are not used in each arrangement?

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*9=81 feet^(2)`

`10*10=100feet^(2)`

or
`11*11=121feet^(2)`

Part B:

For
`9*9=81` 125-81 = 44 tiles are not used

For
`10*10=100` 125-100=25 tiles are not used

For
`11*11=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