Count the number of square tiles s that are in each row.
A
The side length has to be greater than 9 and less than 11 feet.
B
Possible Area
125-A
Unused Tiles
81 square feet
125-81
44 tiles
100 square feet
125-100
25 tiles
121 square feet
125-121
4 tiles
Practice makes perfect
A landscaper has 125 tiles to build a square patio. We want to find the possible arrangements the patio can have if it must have an area of at least 80 square feet.
The measures of the tiles are given in inches, but we will convert them into feet. To do so, we will divide each measure by 12.
12 inches/12 = 1 foot
Since we want a square patio, its area can be calculated by using the formula for the area of a square.
A=s^2
Here, s is the side length of the patio. We need to find a value of s whose square is greater than 80 but less than 125. Remember that 9^2 is equal to 81, which means that the side length of the patio must be at least 9 feet. We can construct a table with the a few possible arrangements for the patio with the values starting at 9.
Possible Side Length
A=s^2
Patio's Area
9 feet
A=9^2
81 square feet
10 feet
A=10^2
100 square feet
11 feet
A=11^2
121 square feet
12 feet
A=12^2
144 square feet
From the table we can see that the side length has to be greater than 9 and less than 11 feet.
We want to calculate how many tiles are not used in each arrangement. Remember that if we want to calculate the area of a square, we can count the number of unit squares s are in each row to calculate its squared power.
A=s^2
Since each tile is one foot in length, the areas calculated in Part A also told us the number of tiles used in each possible arrangement. Then, the difference between 125 and the area of each arrangement will give us the number or unused tiles. We will write the results in another table of values!
