SOLUTION: Hi. This geometry problem really confuses me. Could you please help me solve it with the steps needed. Thank you! A box with rectangular sides has width twice the length of the

Algebra ->  Surface-area -> SOLUTION: Hi. This geometry problem really confuses me. Could you please help me solve it with the steps needed. Thank you! A box with rectangular sides has width twice the length of the      Log On


   

Question 715780: Hi. This geometry problem really confuses me. Could you please help me solve it with the steps needed. Thank you!
A box with rectangular sides has width twice the length of the base. The volume is 24 cubic inches and the total surface area of all six sides is 52 square inches. Write down a (cubic) equation whose solution is the length of the box.
Use L for the length of the box.
Equation: 0 =
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A box with rectangular sides has width twice the length of the base.
The volume is 24 cubic inches and the total surface area of all six sides is 52 square inches.
Write down a (cubic) equation whose solution is the length of the box.
Use L for the length of the box.
:
The volume equation
L * W * H = 24
replace W with .5L; (W is given as half the length)
L*.5L * h = 24
.5L^2 * h = 24
then
h = 24%2F%28.5L%5E2%29 = 48%2FL%5E2, (which we can use for substitution)
:
Surface area equation
2(L*W) + 2(L*H) + 2(W*H) = 52
Simplify, divide by 2
(L*W) + (L*H) + (W*H) = 26
Replace W with .5L
.5L^2 + L*H + .5L*H = 26
.5L^2 + 1.5LH = 26
Replace H with 48%2FL%5E2
.5L^2 + 1.5L*48%2FL%5E2 = 26
Cancel L
.5L^2 + 1.548%2FL = 26
.5L^2 + 72%2FL - 26 = 0
multiply by L to get rid of the denominator, resulting in
.5L^3 - 26L + 72 = 0 is the equation
:
:
I solved this using my Ti83 and got L = 4, then W = 2 and H = 3, that checksout when you find the vol and surface area with these values
:
Did you understand these steps? C