If the perimeter P of a square is expressed as a function of its area A, then it can be written as;
Understand the Problem
The question is asking how to express the perimeter P of a square as a function of its area A. This involves using the formulas for the perimeter and area of a square to find the relationship between them.
Answer
The expression for the perimeter as a function of area is \( P = 4\sqrt{A} \).
Answer for screen readers
The perimeter ( P ) expressed as a function of the area ( A ) is ( P = 4\sqrt{A} ).
Steps to Solve
- Understanding the Area of a Square
The area ( A ) of a square is given by the formula $$ A = s^2 $$ where ( s ) is the length of one side of the square.
- Finding the Side Length
To express ( s ) in terms of ( A ), take the square root of both sides: $$ s = \sqrt{A} $$
- Calculating the Perimeter
The perimeter ( P ) of a square is given by the formula $$ P = 4s $$ Substituting ( s ) from step 2: $$ P = 4\sqrt{A} $$
- Expressing the Perimeter as a Function of Area
Thus, the perimeter ( P ) can be expressed as a function of area ( A ): $$ P = 4\sqrt{A} $$
The perimeter ( P ) expressed as a function of the area ( A ) is ( P = 4\sqrt{A} ).
More Information
This relationship reveals how the perimeter of a square scales with its area. As the area increases, the perimeter increases by a factor that is dependent on the square root, indicating a nonlinear relationship.
Tips
- Forgetting the Square Root: A common mistake is not taking the square root of the area when trying to find the side length of the square.
- Confusing Formulas: Mixing up the formulas for perimeter and area can lead to incorrect final expressions.
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