JEE Main 2021MathematicsApplication of DerivativesMediumMCQ

JEE Main 2021Application of Derivatives Question with Solution

JEE Main 2021 (27 Aug Shift 1)

Question

A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is

Choose an option

Show full solutionCorrect option: C
Correct answer
C103+23

Step-by-step explanation

Let the wire is cut into 2 pieces of length y & 20-y

Therefore side of square will be =y4 and hexagon will be =20-y6

Area of square=y42

Area of hexagon=6×3420-y62

Total area=y216+320-y224

On differentiating,

A'y=2y16+2320-y-124

A'y=0 at y=4033+23

Length of side of regular hexagon=1620-y=1620-4033+23=103+23

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About this question

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