Larger perimeter
Geometry
Level
1
A square and a rectangle have equal areas. Which has a larger perimeter?
Note: Assume that the square and rectangle are not congruent (square has four equal sides and rectangle has two longer sides and two short sides)
Since they have equal areas, they also have equal perimeters.
rectangle
square
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1 solution
Let each side of the square be of a units. Let the rectangle have length l and breadth b .
Given: a 2 = l × b
Just plug in some values that satisfy the given condition. For example;
a = 2 , l = 4 and b = 1
Now substitute these values in their respective perimeter formulas and you'll get a straight answer.