Surface area of a square pyramid is 160cm^2. The area of the lateral triangles is 96cm^2. What is the length of one of the sides?
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Let's call the side length of the square base of the pyramid "s" and the slant height of the pyramid "l".
The formula for the surface area of a square pyramid is:
Total surface area = Base area + (1/2 * Perimeter of base * Slant height)
Given that the total surface area is 160 cm^2 and the area of the lateral triangles is 96 cm^2, we can set up the following equation:
160 = s^2 + 2s * l (equation 1)
96 = 2 * s * l (equation 2)
From equation 2, we can solve for l:
l = 96 / (2s)
l = 48 / s
Now we can substitute this value of "l" back into equation 1:
160 = s^2 + 2s * (48 / s)
160 = s^2 + 96
s^2 = 64
s = 8
Therefore, the length of one of the sides of the square base of the pyramid is 8 cm.