To write an equation that can be used to find the value of the radius
The equation that can be used to find the radius
Given:
Given that the square plot has its side length
Formula Used:
Area of a square:
If the side length ,
Area of a circle:
If the radius,
Calculation:
Since the side length of the square plot is
The square plot is now converted into a circular one without reducing its area.
Thus, the circular plot and the square plot will have the same area as that of the square one.
Suppose that
Then it follows that:
Substitute
Cancel the units from the equation
Thus, the equation that can be used to find the radius of the circular plot:
Conclusion:
The equation that can be used to find the radius
b.
To solve the equation found in part a. to find the radius
The radius
Given Information:
Calculation:
Solve the equation
Now, the radius of a circle cannot be negative.
Then, it follows that:
Conclusion:
The radius
c.
To determine a general rule for the radius
The equation
Given:
Given the side length of the square:
Calculation:
Since the side length of the square plot is
Now, the square plot is converted into a circular one.
So, both the square plot and the circular plot will have the same are.
Suppose that
Then, it follows that;
Now, Substitute
Solve the equation
Now, the radius of a circle cannot be negative.
Then, it follows that:
Now, the equation
Conclusion:
The equation
Chapter 1 Solutions
EBK ALGEBRA 2
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