Answer and Step-by-step explanation:
1. Find the side lengths of a square with an area of [tex]\frac{169}{225} cm^{2}[/tex].
What we know:
- The area of the square.
- The formula for the area of a square. Side times (multiply by) Side, which is also Side Squared [tex]({S}^2)[/tex].
Set the area equal to [tex]({S}^2)[/tex].
[tex]{S}^2 = \frac{169}{225}[/tex]
Take the square root of both sides of the equation to get S (Side).
[tex]\sqrt{{S}^2} = \sqrt{ \frac{169}{225}} \\\\S = \frac{\sqrt{169} }{\sqrt{225} } \\\\S = \frac{13}{15}cm[/tex]<-- This is your answer.
2. Find the radius (distance from a point on the circle to the center of the circle) of a circle using the area 121[tex]\pi yd^2[/tex]
What we know:
- The area of a circle.
- The formula for the area of a circle. [tex]\pi r^2[/tex]
Set the area equal to [tex]\pi r^2[/tex].
[tex]\pi r^2 = 121\pi[/tex]
Divide pi [tex](\pi )[/tex] from both sides of the equation.
[tex]r^2 = 121[/tex]
Take the square root of both sides of the equation.
[tex]\sqrt{r^2} = \sqrt{121} \\\\r = 11[/tex]<-- This is your answer.
3. Find the area of the circular flower garden.
What we know:
- Area of the plot of land: 144
What we can find:
- The side length of a square.
- The radius of a circle.
- The area of a circle.
First, find the side length of the square.
[tex]S^2 = 144\\\\[/tex]
Take the square root of both sides of the equation.
[tex]\sqrt{S^2} = \sqrt{144} \\\\S = 12[/tex]
In this case, the side length of a square will also be the diameter of a circle.
To find the radius, divide the diameter by 2.
[tex]\frac{12}{2} = 6 = r[/tex]
Finally, plug this value into the area of a circle formula and solve.
[tex]\pi r^2\\\\\(3.14) (6)^2\\\\36(3.14) = 113.04cm^2[/tex] <- This is your answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
