# 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.

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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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