Unizor - Geometry3D - Pyramids - Problem 1

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Pyramids - Problem 1

Given a triangular pyramid SABC with side edges that form an arithmetic progression with known first member a and unknown difference x:
SA = a, SB = a+x, SC = a+2x
All angles of the side faces at the apex are right:
∠ASB = ∠BSC = ∠CSA = 90o.
The volume of a pyramid is v.
What are the lengths of side edges?

Answer:
The difference of the arithmetic progression is
x = ( −3a2+√a4+48av ) ⁄4a
So, the side edges are:
SA=a, SB=a+x, SC=a+2x,
where the value of x in terms of a and v is determined above.