JEE Main 2017MathematicsTrigonometric Ratios & IdentitiesMediumMCQ

JEE Main 2017 — Trigonometric Ratios & Identities Question with Solution

JEE Main 2017 (09 Apr Online)

Question

The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60o. If the area of the quadrilateral is 43 sq. units, then the perimeter of the quadrilateral is

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Show full solutionCorrect option: D
Correct answer
D12 units

Step-by-step explanation



cos⁡ 60 o =4+25-c22.2.5

⇒10=29-c2

⇒c2=19

⇒c=19

Now,

cos120°= a 2 + b 2 − c 2 2ab

⇒ -12=a2+b2-192ab

⇒a2+b2-19=-ab

⇒a2+b2+ab=19

Area of quadrilateral  =12×2×5sin⁡60°+12absin⁡120°=43

⇒532+ab34=43

⇒ab4=4-52=32

⇒ab=6

⇒a2+b2=13

⇒a=2, b=3

Perimeter

=2+5+2+3

=12 units

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About this question

This is a previous-year question from JEE Main 2017, covering the Trigonometric Ratios & Identities chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.