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 .

\frac{1 2 inches}{1 2} = 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	$A = 1 0^{2}$	$100$ square feet
$11$ feet	$A = 1 1^{2}$	$121$ square feet
$12$ feet	$A = 1 2^{2}$	$144$ square feet

From the table we can see that the side length has to be greater than $9$ and less than $11$ feet.

Exercise