Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2018
Medium
The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?
- The circle has the largest area.
- BThe square has the largest area.
- CThe equilateral triangle has the largest area.
- DAll the three shapes have the same area.
Explanation
For a fixed perimeter, the shape enclosing the most area is the one closest to a circle — a well-known geometric result (the isoperimetric principle): among shapes with equal perimeter, the circle always encloses the largest area, followed by regular polygons with more sides (square > equilateral triangle).
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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