Question

The rectangle below represents a swimming pool with an area of 30 units^2. Which of the following could be a reasonable value of x?

Answer 1

We can calculate the area of a rectangle by means of the following formula:

`A=b* h`

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:

`A=(3x+1)* x`

By distributing the product we can get rid of the parenthesis:

`A=3x^2+x`

By replacing the value of the area 30 units^2 we get:

`\begin{gathered} 30=3x^2+x \\ 3x^2+x-30=0 \end{gathered}`

We can solve this equation by means of the quadratic equation, like this:

`\begin{gathered} x=\frac{-1\pm\sqrt[]{1^2-4*3*(-30)}}{2*3} \\ x=(-1\pm√(361))/(6) \\ x=(-1\pm19)/(6) \\ x1=(18)/(6)=(9)/(3)=3 \\ x2=(-20)/(6)=-(10)/(3) \end{gathered}`

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