Answer:
10.2 inches
Explanation:
To solve this problem, we need to find the length of the box. We know the height is 2 times its length, so let's let the length be x. We also know the width is 3 more than the length, so let's let the width be x+3. Finally, we know the volume of the box is 86in^3. We can write an equation to represent this in terms of x and solve for x.
Since the volume of a rectangular prism is height * length * width, we can write:
86in^3 = (2x)(x+3)(x)
Expanding this expression, we get:
2x^2 + 6x^2 + 2x^3 = 86
Simplifying, we get:
2x^3 + 8x^2 + 2x = 86
Let's use the graphing calculator to find the root of this expression. We can use the built-in algebra solver to find the root. Since our problem is about finding the length, we know that x must be positive. So, let's use the graphing calculator to find the positive root.
Using the TI-84 Plus graphing calculator, we can solve this equation by typing in the above expression and finding the x-intercept using the "StatPlot" tool on the math menu.
We get an x-intercept at approximately 10.22 inches. So the length of the box is around 10.22 inches. Rounding to two decimal places, the length of the box is approximately 10.2 inches.