Chapter 2.6, Problem 14AYU

To determine

To find:

a. To express the Perimeter $p$ of a square as a function $x$, where $x$ is the length of a wire that is bend into a square.

Answer to Problem 14AYU

Solution:

a. $p\left(x\right)=x$

Explanation of Solution

Given:

A wire of length $‘x’$ is bent into a square.

Calculation:

a. To express the perimeter $‘p’$ of circle as a function $x$:

Since the entire length ‘$x$ ’ is bent into a square, $p\left(x\right)=x$.

To determine

To find:

b. To express the Area $A$ of the square as a function of $x$.

Answer to Problem 14AYU

Solution:

b. $A=\frac{x^2}{16}$

Explanation of Solution

Given:

A wire of length $‘x’$ is bent into a square.

Calculation:

b. To express the $A$ of square as a function $x$:

Side of the square $a=\frac{x}{4}$.

Area of the square $A=a^2 ={\left(\frac{x}{4}\right)}^2$.

Therefore, $A\left(x\right)=\frac{x^2}{16}$.