Final answer:
To find the side length of a square base box with a given volume and height, we first calculate the area of the base with the equation V = A × h. With a volume of 100 cm³ and a height of 5 cm, the side length turns out to be the square root of 20 cm³, which is approximately 4.47 cm, none of the provided answers is correct.
Step-by-step explanation:
The question asks to find the length of one side of the square base of a box with a given volume and height. Knowing that the volume of a box (V) is equal to the area of the base (A) times the height (h), we use the formula V = A × h. Since we are dealing with a square base, A = side × side, or simply side^2. With a volume of 100 cm³ and a height of 5 cm, we can set up the equation 100 cm³ = side^2 × 5 cm. Dividing both sides by 5 cm gives us side^2 = 100 cm³ / 5 cm = 20 cm³. Taking the square root of both sides gives us side = √20 cm³, which is approximately 4.47 cm. The closest answer choice to 4.47 cm is Option A: 2 cm, which seems to be incorrect.