(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a and b are two perpendiculars drawn to the sides from a point on the hypotenuse of a right angled, isoceles triangle.

Find the minimum value of the hypotenuse in terms of a and b.

2. Relevant equations

ABC is a right angled, isoceles triangle, with AC, the hypotenuse, h.

X is a point on AC, from which the perpendiculars a and b are drawn to the sides AB and BC respectively.

AB = BC= h / (sq.root 2)

3. The attempt at a solution

Tried to represent h in terms of a single variable (some angle theta and trigonometric ratios of theta). This would eliminate two variables a and b. With this, h can be differentiated and equated to zero for Minima, and confirming it with 2nd derivative. But could not manage eliminating a and b and converting to a single variable equation.

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# Homework Help: Minima of Hypotenuse

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