Final answer:
To determine the side length of a square-based box without a lid that is 2 cm high with a given total surface area of 48 cm2, set up a quadratic equation based on the sum of the base area and four times the side area. Upon solving, the side length is found to be 4 cm.
Step-by-step explanation:
To find the length of the side of a square-based box without a lid that is 2cm high with a surface area of 48cm2, we first need to understand the surface area of the box.
The surface area of the box consists of the bottom square base and 4 rectangles that form the sides.
The formula for the surface area (SA) of such a box is: SA = base area + 4(side area)
Since the box has a square base, the area of the base is the side length squared (s2), and the area of one side is the side length times the height (s × h). There is no lid, so we only calculate the area of the four sides and base:
SA = s2 + 4(s × h)
We can now set up an equation with the given information and solve for s:
48 cm2 = s2 + 4(s × 2 cm)
48 cm2 = s2 + 8s
We have a quadratic equation which we can solve either by factoring or using the quadratic formula.
In this case, factoring is possible:
s2 + 8s - 48 = 0
(s + 12)(s - 4) = 0
Therefore, s = -12 or s = 4. Since the side length cannot be negative, the length of each side of the box is 4 cm.