Recall that one page of the brochure would be a rectangle of the form
We are told that the area of this rectangle is 30 squared inches. For this rectangle, the area would be

So we have the equation

Also, we are told that the perimeter of the figure is 22 in. Recall that the perimeter of the rectangle is obtained by adding the lengths of the sides of the figure. So we have the equation

Dividing both sides by 2, we get

Using the first equation we have

So if we replace this in the second equation, we have

If we multipy both sides by x, we get

Subtracting 11x from both sides, we get

Recall that given an equation of the form

The solutions are given by the formula
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/rxvf73usjbbwyik14knxdemoz21vfz2ufc.png)
In this case we have a=1, b= -11 and c=30
![x=\frac{-(-11)\pm\sqrt[]{(-11)^2-4\cdot1\cdot30}_{}}{2\cdot1}=\frac{11\pm\sqrt[]{121-120}}{2}=(11\pm1)/(2)](https://img.qammunity.org/2023/formulas/mathematics/college/omoafjveohjru1v5jgrnz7zhenbt2qbd5a.png)
From where we get

and

So, if x=6, we have that

and if x=5, we have that

This means that the longer side is 6 inches long and the shorter side is 5 inches long