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Chapter 1: Problem 63

Write the area \(A\) of a square as a function of its perimeter \(P\).

Short Answer

Expert verified
The area \(A\) of a square as a function of its perimeter \(P\) can be written as \(A = \left(\frac{P}{4}\right)^2.\)

Step by step solution

01

Understand the definitions

Area \(A\) of a square is given by \(A = s^2\) where \(s\) is the length of a single side of the square. Perimeter \(P\) of a square is given by \(P = 4s\) where again \(s\) represents a single side of the square.
02

Express side length in terms of perimeter

From the formula for perimeter \(P = 4s\), it can be rearranged for \(s\) to give \(s = \frac{P}{4}\).
03

Substitute for side length in area formula

Substitute the value of \(s\) derived in step 2 into the area formula to get \(A = \left(\frac{P}{4}\right)^2\).

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