Question

A square garden has a diagonal length of 18 feet. How many 1-foot by 1-foot square planter boxes will fit inside the garden?

Answer 1

To find the number of 1-foot by 1-foot square planter boxes that will fit inside the square garden, use the Pythagorean theorem to find the side length of the garden. Divide the area of the garden by the area of each planter box to determine the number of planter boxes that will fit.

Step-by-step explanation:

To find the number of 1-foot by 1-foot square planter boxes that will fit inside the square garden, we need to determine the area of the garden and divide it by the area of each planter box.

Since the garden is square and the diagonal length is given, we can use the Pythagorean theorem to find the side length of the garden:

Solution:

Let x be the side length of the garden.

By the Pythagorean theorem, we have x² + x² = 18².

2x² = 324.

x² = 162.

x ≈ 12.73 feet (rounded to two decimal places).

The area of the garden is x² = (12.73)² ≈ 162.01 square feet.

Since each planter box is 1 foot by 1 foot, the area of each planter box is 1 square foot.

The number of planter boxes that will fit inside the garden is the area of the garden divided by the area of each planter box:

Number of planter boxes = 162.01 / 1 = 162.01 (rounded to two decimal places).

Therefore, approximately 162 planter boxes will fit inside the square garden.

Answer 2

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,


`d = 18ft`

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.


`{d}^(2) = {l}^(2) + {l}^(2)`


`{18}^(2) = {l}^(2) + {l}^(2)`


`{18}^(2) = 2 {l}^(2)`

Divide both sides by


`{l}^(2) = \frac{ {18}^(2)}{2}`


`{l}^(2) = 162 {ft}^(2)`

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


`\frac{162 \: {ft}^(2) }{1 \: f {t}^(2) } = 162`