CUET · MATHS · PYQ PAPER 2023
If the sum of the lengths of the hypotenuse and one of the other two sides of a right angled triangle is fixed, then the area of the triangle is maximum, when the angle between them is :
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{12}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Let the hypotenuse be \(c\) and the given side be \(a\). The sum is fixed: \(c+a=k\). The other side is \(b = \sqrt{c^2-a^2}\). Area \(A = \frac{1}{2}ab = \frac{1}{2}a\sqrt{c^2-a^2}\). Substitute \(c=k-a\): \(A = \frac{1}{2}a\sqrt{(k-a)^2-a^2} = \frac{1}{2}a\sqrt{k^2-2ka}\). To…
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