Question

The area of a square garden is 100 square meters.

a. Find the length of each side of the garden.
? m area = 100 m2
b. Find the perimeter of the garden.
Please help

Answer 1

a. The length of each side of the garden is 10 m.

b. The perimeter of the garden is 40 m.

Explanation:

A square is a regular polygon with four sides. The area of a square is given by the formula

`Area = width \cdot height`

But since the width and height are by definition the same, the formula is usually written as

`Area = s^2`

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
`m^2` applying the area formula and solving for s, the length of one side, we get that

`100=s^2\\\\s^2=100\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=√(f\left(a\right)),\:\:-√(f\left(a\right))\\\\s=√(100),\:s=-√(100)`

The length can't be negative. Therefore,
`s=√(100)=10`

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:

`Perimeter = 4s`

where s is the length of any one side.

We find that the length of each side is 10 m. Therefore, the perimeter is

`Perimeter = 4s\\\\Perimeter =4 \cdot 10 = 40 \:m`