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If the sum of the lengths of the hypoten...

If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is `pi/3dot`

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To solve the problem, we need to show that the area of a right-angled triangle is maximized when the angle between the hypotenuse and one of the sides is \( \frac{\pi}{3} \) radians (or 60 degrees). ### Step-by-Step Solution: 1. **Define the Triangle**: Let \( ABC \) be a right-angled triangle with the right angle at \( B \). Let \( AB = x \) (one side), \( BC = y \) (the other side), and \( AC = c \) (the hypotenuse). 2. **Establish the Relationship**: ...
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