Sabrinia is building a rectangular raised flower bed. The boards on the two shorter sides are 6 inches thick, and the boards on the two longer sides are 4 inches thick. Sabrina wants the outer length of her bed to be 4 times its height and the outer width to be 2 times its height. She also wants the boards to rise 4 inches above the level of the soil in the bed. What should the outer dimesnions of the bed be if she wants it to hold 3136 cubic inches of soil?

Question

Sabrinia is building a rectangular raised flower bed.  The boards on the two shorter sides are 6 inches thick, and the boards on the two longer sides are 4 inches thick.  Sabrina wants the outer length of her bed to be 4 times its height and the outer width to be 2 times its height.  She also wants the boards to rise 4 inches above the level of the soil in the bed.  What should the outer dimesnions of the bed be if she wants it to hold 3136 cubic inches of soil?

Steve · Answer

If the boards are h inches high, then the soil is (h-4)" deep.

If the outside dimensions are x and y, with x<y,

x=2h
y=4h

So, the inner dimensions are (x-8) and (y-12), and using the given volume,

(h-4)(x-8)(y-12) = 3136
h(2h-8)(4h-12) = 3136
h = 11 inches.

Check:
The outer width is 22
The outer length is 44
The inner width is 14
The inner length is 32
The depth is 7

14*32*7 = 3136

Nice problem! At first I thought not enough information was provided.