A square garden plot measures 180 square feet. A second square garden plot
measures 405 square feet. How many more feet of fence will the second garden
plot require over that required for the first garden plot. But how did they get this???????
Side of first garden plot:
x^2 = 180
x = √180 = 6√5
perimeter is 24√5 or appr 53.67
second garden plot:
y^2 = 405
y = √405
perimeter = 4√405 or appr 80.50
Extra fence needed = 4√405 - 24√5
= appr 26.8 feet
To find out how many more feet of fence the second garden plot requires over the first garden plot, we need to find the difference in the perimeter of the two plots.
The perimeter of a square can be calculated by multiplying the length of one side by 4.
For the first garden plot, we know that it is a square and the area is given as 180 square feet. To find the length of one side, we can take the square root of the area.
√180 = 13.42 feet (approx.)
Now, multiply the length of one side by 4 to find the perimeter of the first garden plot:
Perimeter of first garden plot = 13.42 feet * 4 = 53.68 feet (approx.)
For the second garden plot, we know that it is also a square and the area is given as 405 square feet. Find the length of one side by taking the square root of the area:
√405 = 20.12 feet (approx.)
Multiply the length of one side by 4 to find the perimeter of the second garden plot:
Perimeter of second garden plot = 20.12 feet * 4 = 80.48 feet (approx.)
To find the difference in lengths of fence required, subtract the perimeter of the first garden plot from the perimeter of the second garden plot:
Difference = Perimeter of second garden plot - Perimeter of first garden plot
Difference = 80.48 feet - 53.68 feet
Difference = 26.8 feet (approx.)
Therefore, the second garden plot will require 26.8 feet (approx.) more of fence than the first garden plot.