The perimeter of a square is $80-64y$ units. Which expression can be used to show the side length of one side of the square?
A. $(6i5-4y)$ Each side measures ${ }^{5-4y}$ units.
B. $4(5-4)$ Each side measures $5-4$ units.
C. $4(22-18y)$ Each side measures $20-16y$ units.
D. $(20-16)$. Each side measures $20-16$ units.
Answer (2)
The perimeter of the square is given as 80 − 64 y .
The formula for the perimeter of a square is P = 4 s , where s is the side length.
Divide the perimeter by 4 to find the side length: s = 4 80 − 64 y .
Simplify the expression to find the side length: s = 20 − 16 y . The side length of the square is 20 − 16 y .
Explanation
Understanding the problem We are given that the perimeter of a square is 80 − 64 y units. We need to find the expression that represents the side length of the square.
Formula for the perimeter of a square The perimeter of a square is given by the formula P = 4 s , where P is the perimeter and s is the side length.
Substituting the given perimeter We are given P = 80 − 64 y . Substituting this into the formula, we get 4 s = 80 − 64 y .
Solving for the side length To find the side length s , we divide both sides of the equation by 4: s = 4 80 − 64 y .
Simplifying the expression Now, we simplify the expression: s = 4 80 − 4 64 y = 20 − 16 y .
Final Answer Therefore, the side length of the square is 20 − 16 y units.
Examples
Imagine you're designing a square garden and you know the total length of fencing you have available is 80 − 64 y feet. To figure out how long each side of the garden can be, you need to divide the total fencing length (perimeter) by 4. This problem demonstrates how to calculate the side length of the garden, ensuring you use all your fencing material efficiently and create a symmetrical square space. For example, if y = 0.5 , the side length would be 20 − 16 ( 0.5 ) = 20 − 8 = 12 feet.
The side length of the square is calculated from its perimeter by dividing the perimeter by 4, resulting in an expression of 20 − 16 y . Therefore, option C, which states that each side measures 20 − 16 y units, is the correct choice. No other options fit the derived side length.
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