Respuesta :
Answer:
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
Step-by-step explanation:
You have a block of wood with a depth of x units, a length of 5x units, and a height of 2x units.
height is decreased by 2 units , so height becomes 2x-2
Volume of a block is length times width time height
[tex]volume = x \cdot 5x \cdot (2x-2)[/tex]
[tex]480 = 10x^3-10x^2[/tex]
divide whole equation by 10
[tex]48= x^3-x^2[/tex]
Subtract 48 from both sides
[tex]x^3-x^2-48=0[/tex]
[tex]\left(x-4\right)\left(x^2+3x+12\right)=0[/tex]
[tex]x-4=0[/tex], x=4
[tex]Depth = x= 4 units[/tex]
[tex]length = 5x= 5(4)= 20 \ units[/tex]
[tex]height = 2x-2= 2(4)-2= 6 \ units[/tex]
