Question

The length of a rectangular box is 2 times its width, and its height is 3 ft more than its width. The volume of the box is 130 ft³. Find the width of the box. Round your answer to two decimal places.

Answer 1

The width of the box is approximately 5.84 ft.

Step-by-step explanation:

Let's denote the width of the box as w. According to the given information, the length of the box is 2 times its width, so the length is 2w. The height is 3 ft more than its width, so the height is w+3. The volume of the box is given as 130 ft³, so we can use the formula for the volume of a rectangular box: Volume = Length × Width × Height. Substituting the given values, we get:

130 = (2w) × w × (w+3)

Simplifying this equation, we get a quadratic equation:

2w² + 6w - 130 = 0

To solve this equation, we can use the quadratic formula: w = (-b ± sqrt(b² - 4ac)) / 2a, where a = 2, b = 6, and c = -130. Solving this equation, we find two possible values for the width: w ≈ 5.84 or w ≈ -11.17. Since a negative width doesn't make sense in this context, we can round our answer to two decimal places and conclude that the width of the box is approximately 5.84 ft.