Chapter 8.3, Problem 56PFA

a.

To determine

To find: The perimeter of the square

Answer to Problem 56PFA

  $2x^2-8x$

Explanation of Solution

Given:

Side length of square is $0.5x^2-2x$

Calculation:

The perimeter of a square is four times the side length of the square.

Hence, the perimeter of the square is given by

  $\begin{array}{l}4\left(0.5x^2-2x\right)\\ =2x^2-8x\end{array}$

b.

To determine

To find: The area of the square

Answer to Problem 56PFA

  $0.25x^4-2x^3+4x^2$

Explanation of Solution

Given:

Side length of square is $0.5x^2-2x$

Calculation:

The area of a square is given by ${\left(\text{side}\right)}^2$

Hence, the area of the square is given by

  $\begin{array}{l}{\left(0.5x^2-2x\right)}^2\\ ={\left(0.5x^2\right)}^2-2\cdot 0.5x^2\cdot 2x+{\left(2x\right)}^2\\ =0.25x^4-2x^3+4x^2\end{array}$