Answer:
a. The length of each side of the garden is 10 m.
b. The perimeter of the garden is 40 m.
Step-by-step explanation:
A square is a regular polygon with four sides. The area of a square is given by the formula
[tex]Area = width \cdot height[/tex]
But since the width and height are by definition the same, the formula is usually written as
[tex]Area = s^2[/tex]
where s is the length of one side.
a. To find the length of each side of the garden we know that the area is 100 [tex]m^2[/tex] applying the area formula and solving for s, the length of one side, we get that
[tex]100=s^2\\\\s^2=100\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\s=\sqrt{100},\:s=-\sqrt{100}[/tex]
The length can't be negative. Therefore, [tex]s=\sqrt{100}=10[/tex]
b. In the case of a square, all four sides are the same length, so the perimeter is four times the length of a side. Or as a formula:
[tex]Perimeter = 4s[/tex]
where s is the length of any one side.
We find that the length of each side is 10 m. Therefore, the perimeter is
[tex]Perimeter = 4s\\\\Perimeter =4 \cdot 10 = 40 \:m[/tex]
