Question

A square has an area of 36 ft2. What is the perimeter of the square? Show or explain your answer.

Answer 1

`\boxed {\boxed {\sf 24 \ ft}}`

Explanation:

We are asked to find the perimeter of a square. The perimeter is the sum of all the sides in a shape. Since a square is made of 4 equal sides, we can add the sides or just multiply a side length by 4.

`p=4 s`

1. Side Length

However, we are given the area. We must solve for the side length. The formula for calculating the area of a square is:

`a= s^2`

We know the area of the square is 36 square feet. We can substitute this value in for a.

`36 \ ft^2 =s^2`

We are solving for the side, so we must isolate the variable s. It is being squared. The inverse of a square is the square root, so we take the square root of both sides of the equation.

`\sqrt {36 \ ft^2}= √(s^2)`

`\sqrt {36 \ ft^2}=s`

`6 \ ft =s`

2. Perimeter

Now we know the side length is 6 feet, and we can substitute this into the perimeter formula.

`p=4s`

`p= 4 (6 \ ft)`

Multiply.

`p= 24 \ ft`

The perimeter of the square is 24 feet.