Recalling the Formula for the Perimeter of a Square

Oct 13, 2025 by recoveryshake.com 117 views

Understanding the Problem

The perimeter of a square is given as $80 - 64y$ units. We are asked to find an expression that can be used to show the side length of one side of the square.

Recalling the Formula for the Perimeter of a Square

The perimeter of a square is given by the formula $P = 4s$ , where $P$ is the perimeter and $s$ is the side length.

Applying the Formula to the Given Perimeter

We are given that the perimeter of the square is $80 - 64y$ units. We can set up an equation using the formula for the perimeter:

$P = 4s$ $80 - 64y = 4s$

Solving for the Side Length

To find the side length, we need to isolate $s$ in the equation. We can start by dividing both sides of the equation by 4:

$\frac{80 - 64y}{4} = s$

Simplifying the Expression

We can simplify the expression by evaluating the division:

$20 - 16y = s$

Choosing the Correct Answer

Now that we have found the expression for the side length, we can compare it to the given options.

Option A: $16(5 - 4y)$
Option B: $\frac{16v}{5 - 4}$

Analyzing Option A

Option A is $16(5 - 4y)$ . We can simplify this expression by evaluating the multiplication:

$16(5 - 4y) = 80 - 64y$

This expression is equivalent to the given perimeter, so it is a possible answer.

Analyzing Option B

Option B is $\frac{16v}{5 - 4}$ . However, this expression is not equivalent to the given perimeter, and it also contains a variable $v$ that is not defined in the problem.

Conclusion

Based on our analysis, the correct answer is Option A: $16(5 - 4y)$ . This expression is equivalent to the given perimeter, and it shows the side length of one side of the square.

Final Answer

The final answer is: $\boxed{16(5 - 4y)}$

Discussion

This problem requires the application of the formula for the perimeter of a square and the simplification of algebraic expressions. It also requires the analysis of given options to determine the correct answer.

Practice Problems

Find the perimeter of a square with side length $s$ .
Simplify the expression $2(3x + 2)$ .
Find the side length of a square with perimeter $P = 80 - 64y$ .
The Perimeter of a Square: Q&A ================================

Q: What is the perimeter of a square?

A: The perimeter of a square is the distance around the square. It is given by the formula $P = 4s$ , where $P$ is the perimeter and $s$ is the side length.

Q: How do I find the side length of a square given its perimeter?

A: To find the side length of a square given its perimeter, you can use the formula $s = \frac{P}{4}$ . This will give you the length of one side of the square.

Q: What if the perimeter of the square is given as an expression, such as $80 - 64y$ ? How do I find the side length in this case?

A: If the perimeter of the square is given as an expression, you can set up an equation using the formula for the perimeter: $P = 4s$ . Then, you can solve for $s$ by dividing both sides of the equation by 4. In the case of the expression $80 - 64y$ , you would get $s = 20 - 16y$ .

Q: How do I simplify an algebraic expression like $16(5 - 4y)$ ?

A: To simplify an algebraic expression like $16(5 - 4y)$ , you can use the distributive property to multiply the terms inside the parentheses by the term outside the parentheses. This will give you $80 - 64y$ .

Q: What if I have a variable in my expression that is not defined in the problem? How do I handle this?

A: If you have a variable in your expression that is not defined in the problem, you should not include it in your final answer. In the case of the expression $\frac{16v}{5 - 4}$ , the variable $v$ is not defined in the problem, so you should not include it in your final answer.

Q: Can I use a calculator to find the side length of a square given its perimeter?

A: Yes, you can use a calculator to find the side length of a square given its perimeter. Simply enter the perimeter value into the calculator and divide it by 4 to get the side length.

Q: What if I have a square with a perimeter of $P = 100$ ? How do I find the side length?

A: To find the side length of a square with a perimeter of $P = 100$ , you can use the formula $s = \frac{P}{4}$ . This will give you $s = 25$ .

Q: Can I use the formula for the perimeter of a square to find the side length of a rectangle?

A: No, the formula for the perimeter of a square is only applicable to squares. If you have a rectangle, you will need to use a different formula to find the side length.

Q: What if I have a square with a side length of $s = 10$ ? How do I find the perimeter?

A: To find the perimeter of a square with a side length of $s = 10$ , you can use the formula $P = 4s$ . This will give you $P = 40$ .

Q: Can I use the formula for the perimeter of a square to find the side length of a triangle?

A: No, the formula for the perimeter of a square is only applicable to squares. If you have a triangle, you will need to use a different formula to find the side length.

Q: What if I have a square with a perimeter of $P = 50$ ? How do I find the side length?

A: To find the side length of a square with a perimeter of $P = 50$ , you can use the formula $s = \frac{P}{4}$ . This will give you $s = 12.5$ .

Q: Can I use the formula for the perimeter of a square to find the side length of a circle?

A: No, the formula for the perimeter of a square is only applicable to squares. If you have a circle, you will need to use a different formula to find the side length.

Q: What if I have a square with a side length of $s = 5$ ? How do I find the perimeter?

A: To find the perimeter of a square with a side length of $s = 5$ , you can use the formula $P = 4s$ . This will give you $P = 20$ .

Q: Can I use the formula for the perimeter of a square to find the side length of a trapezoid?

A: No, the formula for the perimeter of a square is only applicable to squares. If you have a trapezoid, you will need to use a different formula to find the side length.

Q: What if I have a square with a perimeter of $P = 200$ ? How do I find the side length?

A: To find the side length of a square with a perimeter of $P = 200$ , you can use the formula $s = \frac{P}{4}$ . This will give you $s = 50$ .