The volume of a rectangular box is x³+16x²+83x+140cm³. The box is x+5 cm long and x+7 cm wide. How tall is the box?
To find the height of the box, we need to divide the volume by the area of the base (length times width).
The volume of the box is given as x³+16x²+83x+140 cm³.
The area of the base is (x+5)(x+7) = x²+12x+35 cm².
So, to find the height (h) of the box, we divide the volume by the area of the base:
h = (x³+16x²+83x+140) / (x²+12x+35)
We can factor the numerator to make it easier to divide:
x³+16x²+83x+140 = (x+5)(x²+11x+28)
Therefore, the height of the box is:
h = (x+5)(x²+11x+28) / (x²+12x+35)
h = (x+5)(x+4)(x+7) / (x+5)(x+7)
h = x+4 cm
So, the height of the box is x+4 cm.