The area of a square vegetable guarden is 60m^2.
a) What is the exact length of each side of the garden?
b) If a fence of a chicken wire is to be constructed around the vegetable garden, what length (to the nearest meter) of chicken wire is needed.
It needs to be answered in surds.
s = 60/√2 = 30√2 m
well, a square has 4 sides, so ...
let the length of each side be s
s^2 = 60
s = √60 = √4*√15 = 2√15
each side is 2√15 m
perimeter = 8√15 m
My bad. I read "diagonal" not "area"
To find the length of each side of the square vegetable garden, we can start by using the formula for the area of a square, which is side squared.
a) Let's let "s" be the length of each side of the garden. So, the equation representing the area of the square can be written as:
s^2 = 60m^2
To find the exact length of each side, we need to find the square root of both sides of the equation:
√(s^2) = √(60m^2)
Simplifying this gives:
s = √60m
Now, we can simplify the square root of 60. Since 60 can be written as a product of its prime factors (2^2 * 3 * 5), we can simplify the expression further:
s = √(2^2 * 3 * 5 * m)
Using the property of square roots (√(ab) = √a * √b), this can be written as:
s = 2√(3m)
Therefore, the exact length of each side of the square garden is 2√(3m).
b) Now, let's determine the length of the chicken wire needed to surround the vegetable garden. Since the fence is placed around the perimeter of the garden, we need to find the perimeter of the square.
The perimeter of a square can be calculated by multiplying the length of one side by 4:
Perimeter = 4s
Substituting the value of s we found in part (a), we have:
Perimeter = 4 * (2√(3m))
Simplifying this gives:
Perimeter = 8√(3m)
To find the length of the chicken wire needed, we need to round the perimeter value to the nearest meter. This will give us the length of the chicken wire needed.
Therefore, the length of chicken wire needed to surround the vegetable garden is approximately 8√(3m) meters (rounded to the nearest meter). In surd form, it can be written as 8√(3m) meters.