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

Sagot :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf 24 \ ft}}[/tex]

Step-by-step 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.

[tex]p=4 s[/tex]

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:

[tex]a= s^2[/tex]

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

[tex]36 \ ft^2 =s^2[/tex]

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.

[tex]\sqrt {36 \ ft^2}= \sqrt{s^2}[/tex]

[tex]\sqrt {36 \ ft^2}=s[/tex]

[tex]6 \ ft =s[/tex]

2. Perimeter

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

[tex]p=4s[/tex]

[tex]p= 4 (6 \ ft)[/tex]

Multiply.

[tex]p= 24 \ ft[/tex]

The perimeter of the square is 24 feet.

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