Maximum area of the Rectangle is:

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Inverse Trigonometric Functions

Question:

A rectangle of length ‘x’ and breadth ‘y’ is inscribed in a semi-circle of fixed radius ‘r’ as shown in the figure given below.

Based on the above information answer the following question:

Maximum area of the Rectangle is:

Options:

2r²

3r²

r²

4r²

Correct Answer:

r²

Explanation:

Area to be maximum ⇒ r² sin 2θ is maximum

Maximum value of sin2θ = 1 . Maximum Area = r²