Sabrina 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

dimensions of the bed be if she wants it to hold 3136 cubic

inches of soil?

The outer dimensions of the flower bed would be 32 in × 14 in × 7 in

Step-by-step explanation:

The outer dimensions of the flower bed is given by:

L is the length of the longer boards

W is the length of the shorter boards

H is the height of the flower bed

As the two shorter sides are 6 inches thick and the two longer sides are 4 inches thick, the inner dimensions are:

L-12: is the inner dimension because there are two shorter boards

W-8: is the inner dimension because there are two longer boards

The boards to rise 4 inches  above the level of the soil in the bed, then:

H-4 is the height of soil

The volume of soil is would be:

(L-12)×(W-8)×(H-4)= 3136

We also know that the outer length must be 4 times its height and the outer width must be 2 times its height, so:

L=4H

W=2H

We solve the equation:

(L-12)×(W-8)×(H-4)= 3136

(4H-12)×(2H-8)×(H-4)= 3136

(8H²-32H-24H+96)×(H-4)= 3136

(8H²-56H+96)×(H-4)= 3136

8H³-56H²+96H-32H²+224H-384= 3136

8H³-88H²+320H-384= 3136

8H³-88H²+320H-384-3136=0

8H³-88H²+320H-3520=0

We divide the equation by 8 in both members:

H³-11H²+40H-440=0

This equation has 1 real solution (H=11) and two complex solutions

The adecuate solution of the problem is H=11

Hence, the outer dimensions of the flower bed are:

L=4H=44 in

W=2H=22 in

Outer dimensions 44 in × 22 in × 11 in

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation: