We can calculate the area of a rectangle by means of the following formula:
[tex]A=b\times h[/tex]
Where b is the length of the base and h is the length of the heigh of the rectangle, by replacing 3x+1 for b and x for h, we get:
[tex]A=(3x+1)\times x[/tex]
By distributing the product we can get rid of the parenthesis:
[tex]A=3x^2+x[/tex]
By replacing the value of the area 30 units^2 we get:
[tex]\begin{gathered} 30=3x^2+x \\ 3x^2+x-30=0 \end{gathered}[/tex]
We can solve this equation by means of the quadratic equation, like this:
[tex]\begin{gathered} x=\frac{-1\pm\sqrt[]{1^2-4\times3\times(-30)}}{2\times3} \\ x=\frac{-1\pm\sqrt{361}}{6} \\ x=\frac{-1\pm19}{6} \\ x1=\frac{18}{6}=\frac{9}{3}=3 \\ x2=\frac{-20}{6}=-\frac{10}{3} \end{gathered}[/tex]
As you can see, we got two solutions, x equals 3 and x equals -10/3, but since x represents the value of the height of the pool and length can only be represented with positive numbers, the correct answer is x equals 3
