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A square and a regular hexagon have equal perimeters. Then their areas are in the ratio:

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2:1

6:3

4:6

answer is D.

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Detailed Solution

Concept-
Here, we will determine the sides of the square and hexagon using the provided perimeters. And using that, we will determine the ratio of their areas.
Question Image

Let a is the side of a square.
Perimeter of a square is

and an area of a square is

.
Let the side of a regular hexagon be b.
Perimeter of a regular hexagon is

and an area of a regular hexagon is

The fact that the perimeters of a square and a regular hexagon are equal is given.
If a square has a side of type a, its perimeter is equal to

. Likewise, if a regular hexagon has a side of type b; its perimeter is equal to

.
According to the given condition, we have
Question Image

When a side of the square is a, the area is

.
In the case where the regular hexagon's side is b, its area is

.
By dividing both areas, it is possible to determine the ratio of the areas of the square and regular hexagon.
Hence, the correct answer is 4)

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