Envelope of Hypotenuse of Right-angled Triangles with Constant Perimeter

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To create a triangle with constant perimeter k, we set one leg equal to a, and then solve for the other side length. The envelop is a circle.

Note that default settings will not set the perimeter equal to k, even when the correct side lengths are entered. The variable k must be set to be larger than a in the variables window so that k is greater than a.

Expressions

Name Input
Perimeter Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image