Expressing the area of a square as a function of its perimeter The text is asking us to state the area A of a square as a function of the perimeter p. If x= the length of a side of a square then the area A of the square =x2 The perimeter p=4x. The solution is p216 I see why the solution is what it is, but I'm struggling to understand how to derive the solution algebraically.

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Expressing the area of a square as a function of its perimeter The text is asking us to state the area A of a square as a function of the perimeter p. If x= the length of a side of a square then the area A of the square =x2 The perimeter p=4x. The solution is p216 I see why the solution is what it is, but I&#039;m struggling to understand how to derive the solution algebraically.

Kayla Kline · Accepted Answer

Perimeter p=4x⇒x=p4. Hence Area a=x2=(p4)2=p216

Raymond Foley · Accepted Answer

The answer is A=P216   The perimeter P of a square is sum of its sides s: P=s+s+s+s=4s   The area A of a square with side s is: A=s⋅s=s2   Step 1: Solve s from the formula for the perimeter.   Step 2: substitute s from the formula for the perimeter into the formula for the area.   Step 1:   P=4s   s=P4   Step 2:   A=s2   s=P4   A=(P4)2   A=P242   A=P216

nick1337 · Accepted Answer

Let&#039;s express the area of the square in terms of its perimeter. Explanation: If s= side of the square, then, Area of the square (A)=s⋅s (1) Perimeter of the square (p)=4s ⇒s=p4 Putting this value of s in equation (1), A=(p4)×(p4) =p216 Therefore, the area of a square as a function of its perimeter p is equal to p216.

Mr Solver · Accepted Answer

To express the area A of a square as a function of its perimeter p, we can follow these steps algebraically:1. Start with the equation for the perimeter of a square: p=4x, where x is the length of a side of the square.2. Solve the equation for x to express it in terms of p: x=p4.3. Substitute the value of x in the equation for the area of a square: A=x2=(p4)2.4. Simplify the expression for A by squaring (p4): A=p216.Therefore, the area A of the square can be expressed as a function of its perimeter p using the formula A=p216.

Nick Camelot · Accepted Answer

Step 1: Let&#039;s define the variables:- A as the area of the square.- p as the perimeter of the square.- x as the length of a side of the square.Step 2: Write equations for the given relationships:We know that the area A of a square is given by A=x2.Similarly, the perimeter p of a square is given by p=4x.Step 3: Solve for x in terms of p:From the equation p=4x, we can isolate x by dividing both sides by 4:p4=xStep 4: Substitute the value of x in the equation for A:Now, substitute the value of x in terms of p into the equation A=x2:A=(p4)2Step 5: Simplify the expression:To simplify, square the term inside the parentheses:A=p216Therefore, the area A of a square can be expressed as the function A(p)=p216, where p is the perimeter of the square.

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