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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2024 · Mathematics · Application of Derivatives

The maximum area of rectangle inscribed in a circle of diameter R is

The maximum area of rectangle inscribed in a circle of diameter RR is

Options

  1. AR2R^2
  2. BR22\frac{R^2}{2}
  3. CR24\frac{R^2}{4}
  4. DR28\frac{R^2}{8}

Correct answer

B. R22\frac{R^2}{2}

Step-by-step solution

According to question, Diameter =R=R Diagonals, d1=d2=Rd_1=d_2=R Max Area of rectangle (any quadrilateral) =12d1×d2=12×R×R=R22\begin{aligned} \text{ Max Area of rectangle (any quadrilateral) } & =\frac{1}{2} d_1 \times d_2 \\ = & \frac{1}{2} \times R \times R=\frac{R^2}{2} \end{aligned}$$
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