SOLUTION: a rectangular solid has a volume of 640 cu.units.the width is 3 units more than the height and the length is 1 unit more than three times the height. find the dimension of the soli

Algebra ->  Volume -> SOLUTION: a rectangular solid has a volume of 640 cu.units.the width is 3 units more than the height and the length is 1 unit more than three times the height. find the dimension of the soli      Log On


   



Question 338802: a rectangular solid has a volume of 640 cu.units.the width is 3 units more than the height and the length is 1 unit more than three times the height. find the dimension of the solid
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a rectangular solid has a volume of 640 cu.units.the width is 3 units more than
the height and the length is 1 unit more than three times the height.
find the dimension of the solid
:
Let x = the height
then
(x+3) = width
and
(3x+1) = length
;
x(x+3)(3x+1) = 640
x(3x^2 + x + 9x + 3) = 640
x(3x^2 + 10x + 3)
3x^3 + 10x^2 + 3x - 640 = 0
:
Plot this equation, find the x intercept
+graph%28+300%2C+200%2C+-6%2C+10%2C+-700%2C+300%2C+3x%5E3+%2B+10x%5E2+%2B+3x+-+640%29+
:
x = 5 is the height
then
5 + 3 = 8 is the width
and
3(5) + 1 = 16 is the length
:
Check: 5 * 8 * 16 = 640 cu/units