Respuesta :
Answer:
The actual area of the garden is 1256 square feet.
Step-by-step explanation:
Given:
A gardener is designing a circular garden.
On the blueprint, the garden has a diameter of 16 centimeters.
The blueprint has a scale of two centimeters to five feet.
Now, to find the actual area of the garden.
Let the actual diameter of the garden be [tex]x\ feet.[/tex]
And the diameter of the garden on blueprint = [tex]16\ centimeters.[/tex]
As, given:
The blueprint has a scale of two centimeters to five feet.
2 centimeters is equivalent to 5 feet.
Thus, 16 centimeters is equivalent to [tex]x\ feet.[/tex]
Now, to get the actual diameter by using cross multiplication method:
[tex]\frac{2}{5} =\frac{16}{x}[/tex]
By cross multiplying we get:
[tex]2x=80[/tex]
Dividing both sides by 2 we get:
[tex]x=40\ feet.[/tex]
Thus, the actual diameter of the garden is 40 feet.
Now, to get the area of the garden we get the radius and then put the formula of area:
Radius = [tex]\frac{Diameter}{2}[/tex]
Radius(r)= [tex]\frac{40}{2}=20\ feet.[/tex]
[tex]Area =\pi r^2.[/tex]
[tex]Area=3.14\times 20^2[/tex]
[tex]Area=3.14\times 400[/tex]
[tex]Area=1256\ square\ feet.[/tex]
Therefore, the actual area of the garden is 1256 square feet.
