A wire of length 20m 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…
JEE Main 2021 — Mathematics Calculus
2021mcqmedium
A wire of length 20m 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
Official previous-year question
Held on 27 Aug 2021 · Verified 6 Jul 2026.
Options
A
2+3310
B
3+35
C
3+2310
D
2+35
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Solution
Let the wire is cut into 2 pieces of length y&20-y
Therefore side of square will be =4y and hexagon will be =620−y
Area of square=(4y)2
Area of hexagon=6×43(620−y)2
Total area=16y2+243(20−y)2
On differentiating,
A′(y)=162y+2423(20−y)(−1)
A′(y)=0aty=3+23403
Length of side of regular hexagon=61(20−y)=61(20−3+23403)=3+2310
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