Chapter 8.6, Problem 50HP

To determine

To find: The perimeter of the square.

Answer to Problem 50HP

  $\left(12x+20y\right)\text{inches}$

Explanation of Solution

Given:

The area of square is given by $9x^2+30xy+25y^2$ square inches

The dimensions of the square are binomials with positive integers.

Calculation:

The area of square is $9x^2+30xy+25y^2$ square inches.

Write this polynomial in factored form

This polynomial can be rewritten as

  ${\left(3x\right)}^2+2\cdot 3x\cdot 5y+{\left(5y\right)}^2$

Using the formula ${\left(a+b\right)}^2=a^2+2ab+b^2$ , this polynomial should be equal to

  ${\left(3x+5y\right)}^2$

Now, the area of a square is the equal to the square of the side length.

Hence, dimensions of the square are $\left(3x+5y\right)$ inches.

Hence, perimeter of the square is four times the dimension of the square

  $\begin{array}{l}4\left(3x+5y\right)\\ =\left(12x+20y\right)\text{inches}\end{array}$