Nancy is planting cucumbers in a small garden. Before planting, Nancy adds a layer of soil to the garden.
The picture shows an upside-down right-angled triangle. The angle of the top vertex is 45 degrees, and the angle of the left vertex is 45 degrees. The length of the hypotenuse is 14 ft.
Approximately how many square feet is needed to cover the garden with a layer of soil?
To find the area of the garden, we need to find the length of the two legs of the right-angled triangle.
Given that the hypotenuse is 14 ft, we can use the Pythagorean theorem to find the length of the legs.
Let's call the length of one leg x.
Using the Pythagorean theorem, we have:
x^2 + x^2 = 14^2
2x^2 = 196
x^2 = 196/2
x^2 = 98
x ≈ √98
x ≈ 9.89 ft
The area of the triangle can be calculated as:
Area = (1/2) * base * height
= (1/2) * x * x
= (1/2) * (9.89 ft) * (9.89 ft)
≈ 48.96 ft^2
So approximately 48.96 square feet of soil is needed to cover the garden with a layer of soil.