JEE Main 2021MathematicsProperties of TrianglesMediumMCQ

JEE Main 2021 — Properties of Triangles Question with Solution

JEE Main 2021 (20 Jul Shift 1)

Question

If in a triangle ABC, AB=5 units, ∠B=cos-135 and radius of circumcircle of ∆ABC is 5 units, then the area (in sq. units) of ΔABC is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C6+83

Step-by-step explanation

We have,

As,

cosB=35⇒sinB=45

Given:

R=5

By sine rule, we have

csinC=2R

⇒510=sinC

⇒C=30°
Now,

bsinB=2R

⇒b=45×10=8

Now, by cosine formula

cosB=a2+c2-b22ac

⇒35=a2+25-6425a

⇒a2-6a-39=0

⇒a=6±1922=6±832

⇒a=3+43 

(Reject a=3-43<0)

Now, Δ=abc4R=3+43·8·54·5=23+43

⇒Δ=6+83 sq. units.

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About this question

This is a previous-year question from JEE Main 2021, covering the Properties of Triangles 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.