The apothem of a square having its area numerically equal to its perimeter is compared with the apothem of an equilateral triangle having its area numerically equal to its perimeter. The first apothem will be

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equal to the second

times the second

answer is A.

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Detailed Solution

Concept: First, we need to find the side lengths of the square and the equilateral triangle under the given conditions. Next, we need to calculate and compare both square and equilateral triangle apothems.
It has been found that the apothem of a square whose area is numerically equal to its perimeter is compared to the apothem of an equilateral triangle whose area is numerically equal to its perimeter.
What is Apotema-
The apothem distance (sometimes abbreviated as apo) of a regular polygon is the line segment from the center to one midpoint on that side. Similarly, it is a line drawn perpendicular to one of its sides from the center of the polygon. The term "apothem" may also refer to the length of this line segment. First, find the side length of the square under the given conditions. For this reason,
Let's assume that the length of one side is x.

(given) ... (1)
A square with sides has twice the area is

and four times the perimeter is

. From equation (1) , it becomes as follows.

Dividing both sides by x gives:

Now, in the case of a square, the apothem distance

is half the length of the side. therefore,

Then calculate the length of the sides of the equilateral triangle for the given conditions. we,

(given) ... (2)
Suppose the length of one side is y. For an equilateral triangle with a side of y, the area is

and the perimeter is 3y. From equation (2) , it becomes as follows.

Dividing both sides by y gives:

Divide both sides by

………..(3)
For an equilateral triangle, the apothem distance