Chapter 8.4, Problem 69PFA

To determine

To find: The area of the field.

Answer to Problem 69PFA

  $\left(x^4+4x^2+4\right)\text{Sq}\text{. yards}$

Explanation of Solution

Given:

The perimeter of a square field is $4x^2+8$ yards.

Calculation:

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

Hence, the side length should be one fourth the perimeter of the square.

Thus, the side length of the square is given by

  $\begin{array}{l}\frac{4x^2+8}{4}\\ =\left(x^2+2\right)\text{yards}\end{array}$

Therefore, the area of the square is given by

  $\begin{array}{l}{\left(\text{Side}\right)}^2\\ ={\left(x^2+2\right)}^2\\ =\left(x^4+4x^2+4\right)\text{Sq}\text{. yards}\end{array}$