A point on the hypotenuse of a triangle is at distance and from the sides of the triangle

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

9. A point on the hypotenuse of a triangle is at distance

a

and

b

from the sides of the triangle. Show that the minimum length of the hypotenuse is

\left(a^{\frac{2}{3}}+b^{\frac{2}{3}}\right)^{\frac{3}{2}}