Answer
$x = 4.87$ in
Work Step by Step
Area of a rectangle is $$\text{Area}=\text{length}\cdot\text{width}.$$ Substituting the area, length, and width, we get: $$288 = (2x+10)(3x).$$ Simplifying the right side, we get: $$288 = 6x^2+30x.$$ Factoring out $6$, we get: $$288 =6(x^2+5x).$$ Dividing $6$ on both sides, we get: $$48 = x^2+5x.$$ Subtracting $48$ on both sides, we get: $$x^2+5x-48 = 0.$$ Using the quadratic formula, we get $$x=\frac{-5\pm\sqrt{25+192}}{2}$$, therefore the solutions are $\approx4.865$ and $-9.865$.
Knowing the length of a rectangle must be positive, $4.865$ is the only solution. Rounded to the nearest hundredth, the final answer is $4.87$.
