Question

A white label is wrapped around a rectangular box with square bases covers 80 percent of the lateral surface area of the box. Find the length x of the box.

Answer 1

Answer:

The box is 7.5 in long.

Step-by-step explanation:

Calculate the total surface area of the sides of this box (neglecting the ends).

If the base is 3" by 3" and the length of the box is 6", then the total surface area (without ends) is 4 times 3" by x, or  12x in².  80% of this "lateral surface area" is 0.80(12x in²), or 9.60x in° and this 9.60x in² represents the surface area covered b y the label.  That label surface area is 4(3 in by 6 in), or 72 in²

Equating 9.60x in² and 72 in² and solving for x yields  x = (72 in²) / (9.60 in²:

x = 7.5 in

The box is 7.5 in long.