Answer:
x= 3 inches
Step-by-step explanation:
-The volume of a box is given by the formula:
[tex]V=lwh\\\\l-length\\w-width\\h-height[/tex]
-We are given the dimensions h=x+2, l=2x+5 and w=4x-1.
We substitute this values in the formula and equate to the volume value.
[tex]V=lwh\\\\605=(x+2)(2x+5)(4x-1)\\\\605=8x^3+34x^2+31x-10[/tex]
#We take the values to the same side and equate to zero;
[tex]8x^3+34x^2+31x-615=0\\\\\\\#Factor\\\\\\(x-3)(8x^2+58x+205)=0[/tex]
#Applying the zero factor principal to obtain the different values of x:
[tex](x-3)=0\\\\\therefore x=3\ \ \ \ \ \ ...i\\\\(8x^2+58x+205)=0[/tex]
#We use the quadratic formula to solve the two other values of x:
[tex](8x^2+58x+205)=0\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\=\frac{-58\pm\sqrt{58^2-4\times 8\times 205}}{2\times 8}\\\\x=-3.625+3.533i \ and \ x=-3.625-3.533i[/tex]
The two other values are negatives. Ignore them since length cannot be a negative.
The only reasonable value of x is x=3
#We substitute in the formula to validate:
[tex]V=lwh\\\\=(x+2)(2x+5)(4x-1)\\\\=(3+2)(2*3+5)(4*3-1)\\\\=605[/tex]
Hence, the value of x is 3 inches
