Answer:
The length = The width = The height ≈ 5.8 cm
Explanation:
The volume of a rectangular pyramid, V = l × w × h
The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200
∴ l × h + w × h + l × w = 200/2 = 100
We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;
At maximum volume, l = w = h
∴ l × h + w × h + l × w = 3·l² = 100
l² = 100/3
l = 10/√3
Therefore, the volume, v = l³ = (10/√3)³
The length = The width = The height = 10/√3 cm ≈ 5.8 cm