SOLUTION: The volume of a rectangular solid is 990 cubic cm and its total area is 675 sq. cm. If its altitude is 20 cm, find the dimensions of the base.

Algebra ->  Surface-area -> SOLUTION: The volume of a rectangular solid is 990 cubic cm and its total area is 675 sq. cm. If its altitude is 20 cm, find the dimensions of the base.      Log On


   

Question 946067: The volume of a rectangular solid is 990 cubic cm and its total area is 675 sq. cm. If its altitude is 20 cm, find the dimensions of the base.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be the bottom dimensions.
Volume is 20xy=990.
Total area is 2%2A20x%2B2%2A20y%2B2%2Axy=675.

Simplify the system.
system%282xy=99%2C40x%2B40y%2B2xy=675%29

A bit of some algebra steps, but solve the first equation for either variable and substitute into the second equation.--------------BUT recognize that both equations have a term, 2xy. Make use of that!!

40x%2B40y%2B%2899%29=675, substituting for 2xy.
40x%2B40y-675%2B99=0
40x%2B40y-576=0
NOW use the first equation again but solved for either variable in terms of the other variable: y=99%2F%282x%29.
Substitute for that variable.
40x%2B40%2899%2F%282x%29%29-576=0
40x%2B20%2A99%2Fx-576=0
40x%5E2%2B198-576x=0----Do you know what was done for this step?
20x%5E2-288x%2B99=0

Not sure if that is factorable. Find discriminant.
288%5E2-4%2A20%2A99
82944-8%2A99%2A10
82944-7920
67104
9%2A7456=9%2A4%2A1864=9%2A4%2A4%2A466=9%2A4%2A4%2A2%2A233, the big factor being prime.
Discriminant is highlight_green%28%283%2A4%29%5E2%2A%282%2A233%29%29.

x=%28288%2B-+sqrt%283%5E2%2A4%5E2%2A466%29%29%2F%28400%29
x=%28288%2B-+12%2Asqrt%28466%29%29%2F400
highlight%28x=%2872%2B-++3%2Asqrt%28466%29%29%2F100%29
Not really finished but more than half the way to it.