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Question

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:

A
equal to the second
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B
4/3 times the second
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C
23 times the second
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D
23 times the second
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E
indeterminately related to the second
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Solution

The correct option is A equal to the second
Let s1 be the side of the square, a1 its apothem; then s21=4s1 and since 2a1=s1, we have 4a21=8a1 or a1=2. Let s2 be the side of the equilateral triangle, h its altitude and a2 its apothem; then s2234=3s2. Since h=3a2, and s2=2h3=6a23, we have (3622/3)3/4=3.6a2/3anda2=2=a1

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