ANSWER
162 boxes
EXPLANATION
The diagonals of the square garden has length 18 feet.
We want to find how many 1-foot by 1-foot square planter boxes that will fit inside the garden.
This is the same as finding the area of the square garden given the diagonal,
[tex]d = 18ft[/tex]
and then diving by 1 sq. ft
Let the side lengths of the square be l feet each.
Then the diagonal together with any two sides forms an isosceles right triangle.
We can apply the Pythagoras Theorem, which says that, the sum of the squares of the two shorter legs equals the square of the hypotenuse ( the diagonal) in this case.
[tex] {d}^{2} = {l}^{2} + {l}^{2} [/tex]
[tex] {18}^{2} = {l}^{2} + {l}^{2} [/tex]
[tex] {18}^{2} = 2 {l}^{2} [/tex]
Divide both sides by
[tex] {l}^{2} = \frac{ {18}^{2}}{2} [/tex]
[tex]{l}^{2} = 162 {ft}^{2} [/tex]
The area of the square garden is 162 ft²
The number of 1 foot by 1 foot square planter boxes that can fill this garden is
[tex] \frac{162 \: {ft}^{2} }{1 \: f {t}^{2} } = 162[/tex]
