34. Construct a Triangle ABC Given the Length of AB and the Sum and Product of the Other Two Sides
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This Demonstration shows how to construct a triangle given the length
of the side
, the sum of the lengths of the other two sides
and their product
. The numbers
and
satisfy the quadratic equation
. It is solved graphically using Descartes's method for constructing roots of polynomials.
Contributed by: Izidor Hafner and Marko Razpet (September 2018)
Open content licensed under CC BY-NC-SA
Details
Let . Thus
or
. The triangle inequality is
, which is
. Suppose
; the triangle inequality
implies
.
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