A wire of length x is bent into the shape of a square.
(a) Express the perimeter of the square as a function of x.
(b) Express the area of the square as a function of x.
A wire of length x bent into a square would make each side $\displaystyle \frac{1}{4}x$
Perimeter of the square $\displaystyle P(x)=\frac{1}{4}x+\frac{1}{4}x+\frac{1}{4}x+\frac{ 1}{4}x=\frac{4}{4}x=x$
Area of the square would be $\displaystyle A(x)=\left(\frac{1}{4}x\right)^2=\frac{1}{16}x^2$