4. Surface area of a square pyramid is 160cm^2. The area of the lateral triangles is 96cm^2. What is length of one of the sides.
Let's denote the side length of the base of the square pyramid as s and the slant height of one of the lateral faces as h.
The surface area of the square pyramid is given by:
Surface Area = Area of Base + 2 * Area of Lateral Faces
160cm^2 = s^2 + 2 * 96cm^2
From the second equation, we can calculate the side length s as follows:
160cm^2 = s^2 + 192cm^2
s^2 = 160cm^2 - 192cm^2
s^2 = -32cm^2
s = √(-32)
s = 4√2 cm
Therefore, the length of one of the sides of the base of the square pyramid is 4√2 cm.