Final answer:
To find the width of the box (X), we use the volume formula for a rectangular box (Volume = length × width × height) with the given height (5ft) and the expression for length ('the length is 3ft longer than twice the width X'). Solving the resulting equation will give us the width, and from there we can find the length to ensure the volume is 450 cubic feet.
Step-by-step explanation:
Finding the Dimensions and Volume of a Rectangular Box-
To solve for the dimensions and volume of the rectangular box, we use the given height and the relationship between the length and the width. The height is given as 5ft. The length, according to the problem, is defined as 'the length is 3ft longer than twice the width X'. Thus we can express the length (L) in terms of the width (X) as L = 2X + 3. We are also given that the volume of the box is 450 cubic feet.
To find the width (X), we can use the formula for the volume of a rectangular box, which is Volume = length × width × height. Substituting the given values and the expression for L, we have:
Volume = (2X + 3) × X × 5
This leads to the equation:
450 = (2X + 3) × X × 5
By solving this equation for X, we determine the width, and substituting back, we can find the length. From there, we can confirm that the calculated dimensions give us a volume of 450 cubic feet.