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If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of traingle is maximum when the angle between them is \( \large\frac{\pi}{3} \).
cbse
class12
modelpaper
2012
sec-c
q24
math
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asked
Dec 29, 2012
by
thanvigandhi_1
edited
Jul 18, 2013
by
sreemathi.v
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If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is \( \frac{\pi}{3} \)
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Prove that the area of a right-angled triangle of given hypotenuse is maximum when it is isosceles.
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A point on the hypotenuse of a right-angled triangle is at distances a and b from the sides. Show that length of the hypotenuse is at least \( (a^{\large\frac{2}{3}}+b^{\large\frac{2}{3}})^{\large\frac{3}{2}} \)
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