Final answer:
To find the height x of a rectangular prism where the surface area equals the volume, we use the formulas for surface area and volume, set them equal to each other, and solve for x. With a length of 11 and width of 3, we find that the height x equals 13.2 units after solving the equation.
Step-by-step explanation:
We are asked to find the height x of a rectangular prism where the surface area and the volume are the same. Given the length is 11 units and the width is 3 units, we can use the formulas for surface area and volume of a rectangular prism: Surface Area (SA) = 2lw + 2lh + 2wh and Volume (V) = lwh, where l is length, w is width, and h is height.
To solve the problem, set the surface area equal to the volume:
2lw + 2lh + 2wh = lwh
Substitute the given values (l=11, w=3) into the equation:
2(11)(3) + 2(11)x + 2(3)x = (11)(3)x
Solve for x.
66 + 22x + 6x = 33x
66 = 33x - 22x - 6x
66 = 5x
x = 66 / 5
x = 13.2
The height x is therefore 13.2 units.