Project ForgeEngineering Mathematics
Calculus
GATE 2023
Easy
The smallest perimeter that a rectangle with area of 4 square units can have is ______ units.
8(± 0.1 accepted)
Explanation
For fixed area A=xy=4, perimeter P=2(x+y)=2(x+4/x). Minimizing via dP/dx=2(1−4/x²)=0 gives x²=4, x=2, so y=2 as well (a square). Minimum perimeter=2(2+2)=8.
Source: GATE ME 2023 Official Paper (2023)
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