A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is $(a^{\frac{2}{3}} + b^{\frac{2}{3}})^{\frac{3}{2}}$ .

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A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is

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

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A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is

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

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