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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2018 · Mathematics · Application of Derivatives

Paragraph: Three sides of a trapezium are each equal to 6 cm. Let α...

Paragraph: Three sides of a trapezium are each equal to 6 cm. Let \alpha \in \left(0, \frac{\pi}{2}\right)be the angle between a pair of adjacent sides.
Question: What is the maximum area of the trapezium?

Options

  1. A363cm236 \sqrt{3} \mathrm{ cm}^2
  2. B303cm230 \sqrt{3} \mathrm{ cm}^2
  3. C273cm227 \sqrt{3} \mathrm{ cm}^2
  4. D243cm224 \sqrt{3} \mathrm{ cm}^2

Correct answer

C. 273cm227 \sqrt{3} \mathrm{ cm}^2

Step-by-step solution

 Area =(6+x)36−x2=(6+3)36−32=936−9=927=99×3=273\begin{aligned} & \text{ Area }=(6+x) \sqrt{36-x^2} \\ & =(6+3) \sqrt{36-3^2}=9 \sqrt{36-9}=9 \sqrt{27} \\ & =9 \sqrt{9 \times 3}=27 \sqrt{3}\end{aligned}
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