Respuesta :
Answer:
Length = 20 inches
Width = 10 inches
Height = 9 inches
Step-by-step explanation:
Assume the width to be equal to 'w' inches.
It is given that the length of the cake to be twice of width. So,
Length of cake = 2 × (width of cake) = 2w
It is also given that the height of cake to be 1 inch less than the width of cake. So,
Height of cake = (width of cake) - 1 = w-1
Volume of cake = (Length) × (Breadth) × (Height)
Volume of cake is given to be as 1800 inch cube.
Therefore, 1800 = (2w) × (w) × (w-1)
900 = (w) × (w) × (w-1)
[tex]900=\textrm{w}^{3}-\textrm{w}^{2}[/tex]
[tex]\textrm{w}^{3}-\textrm{w}^{2}-900=0[/tex]
To solve cubic equation there is only one way is to get the first root* by hit and trial. (you will hit the bulls-eye only by practice)
Let w=10 So,
[tex](10)^{3}-(10)^{2}-900=0\\1000-100-900=0\\1000-1000=0\\0=0[/tex]
So the solution is w=10.
Therefore the width = w = 10 inches
Length = 2w = 20 inches
Height = w-1 = 9 inches
(*As you know that a cubic equation have three roots. In them there are two cases possible: one root is real and rest two imaginary or all the three are real. Here in this case only one root is real and other two are imaginary.In this question the factorized form of this cubic equation is [tex](w-10)(w^{2}+9w+90)=0[/tex]. By this factorized form you can conclude that one root is 10 and the roots of the quadratic equation are imaginary (as [tex]D=9^{2}-4\times1\times90<0[/tex]). In this only real root can become solution as the solution gives width which is a real quantity. So, the only real solution is w=10 )
