The perimeter, P, of a square is a function of the length of...

The perimeter, $P$, of a square is a function of the length of its side, $s$. a) Write an equation using function notation to describe this relationship between $P$ and $s$. b) If the length of a side is given in feet, find $P(2)$ and explain what this means in the context of the problem. c) If the length of a side is given in centimeters, find $P(11)$ and explain what this means in the context of the problem. d) What is the length of each side of a square that has a perimeter of 18 inches?

The perimeter, $P$, of a square is a function of the length of its side, $s$.
a) Write an equation using function notation to describe this relationship between $P$ and $s$.
b) If the length of a side is given in feet, find $P(2)$ and explain what this means in the context of the problem.
c) If the length of a side is given in centimeters, find $P(11)$ and explain what this means in the context of the problem.
d) What is the length of each side of a square that has a perimeter of 18 inches?

Key Concepts

Square Properties

A square is a geometric shape that has four equal sides and four right angles. The concept of a square is important because its symmetry simplifies many calculations, including its perimeter, which is simply the sum of all its four sides.

Function Notation

Function notation is a mathematical way to represent relationships between quantities by defining a function with an input and output. For instance, using P(s) to denote the perimeter of a square as a function of its side length s illustrates how changes in s affect the perimeter.

Linear Relationships

A linear relationship is characterized by a constant rate of change between two variables, expressed by a multiplication factor. In the case of a square, the perimeter is a linear function of the side length, such that doubling the side length will double the perimeter.

Unit Analysis

Unit analysis involves ensuring consistency in the measurements used throughout a problem. It is crucial to recognize and maintain the proper units, whether using feet, centimeters, or inches, to correctly interpret and compare physical quantities like side lengths and perimeters.

Algebraic Equation Solving

Algebraic equation solving is used to find unknown values by manipulating equations. For example, when given a particular perimeter, one can rearrange the equation relating the side length and perimeter of a square to solve for the side length.

Transcript

00:01 So in the question we have a perimeter for a square which is denoted as p and we have the length of one side which is s so for the question a we have to find out the relationship between p and s let's go so we know for the square the perimeter of the square will be four times the one side the length of one side of the square so we can write it like this p of s is equal to four times s so this is the equation for perimeter and side so for the question b we have given the one the length of one side so which is denoted as p of 2 is given so we have to find out the perimeter for this so we know here from the question a the equation will be p of s is equal to 4 s so we can write as well 4 into so the parameter will be 8 feet so here in the question they have given that the one side of a square which is two feet we have to find out the perimeter for this two feet for this square which is that one side of it is two feet so that's what the question has asked for so this is the answer in the question c we have one side given which is p of 11 so we have to find out the parameter for this certain site so we know from the equation p of s is equal to 4 s so we can write 4 times 11 so it will be 44 centimeter so in this question they have have asked for perimeter of the square and they have given that p of 11 which is which means what is the perimeter of the square for if the one side of the square is 11 centimeter so that so what the question means so the one perimeter of this square will be 44 centimeter and for the question they have given a certain perimeter so we have to find out the length of the square one side length of each side of the square so we know the length of each length of each square is the same so from the equation we can write that p of s is equal to 18 as the perimeter is given so we can write p of s is equal to 4 s so we can write v s of s as 4 s is equal to 80 so if we solve the equation we'll get the value of s and we'll get the value of each side so thus s will be 4 .5 so the unit will be an inch so yes the question d we have the length of each sides of a square is 4 .5 inches so this is the answer for this question...

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