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If the area of an equilateral triangle is equal to the area of a square prove that the perimeter of the equilateral triangle is greater than the perimeter of the square.?
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If the area of an equilateral triangle is equal to the area of a squar...
Equilateral Triangle vs. Square: Area and Perimeter Comparison
To prove that the perimeter of an equilateral triangle is greater than that of a square when their areas are equal, we can start by defining the areas of both shapes.
Area of an Equilateral Triangle
- The area (A) of an equilateral triangle with side length 's' is given by:
- A = (sqrt(3) / 4) * s^2
Area of a Square
- The area (A) of a square with side length 'a' is:
- A = a^2
Setting the Areas Equal
- Given that the areas are equal:
- (sqrt(3) / 4) * s^2 = a^2
Solve for Side Lengths
- Rearranging the equation for 'a':
- a = sqrt((sqrt(3) / 4) * s^2)
- a = (s * sqrt(sqrt(3) / 4))
Perimeters of Both Shapes
- The perimeter (P) of the equilateral triangle is:
- P_triangle = 3s
- The perimeter of the square is:
- P_square = 4a
Substituting for 'a'
- Substituting the expression for 'a' into the perimeter of the square:
- P_square = 4 * (s * sqrt(sqrt(3) / 4))
Comparing Perimeters
- To see if P_triangle > P_square:
- P_triangle = 3s
- P_square = 4 * (s * sqrt(sqrt(3) / 4))
- Since sqrt(sqrt(3) / 4) is less than 1, it follows that:
- 3s is greater than 4 * (s * sqrt(sqrt(3) / 4))
Conclusion
- Therefore, the perimeter of the equilateral triangle is indeed greater than the perimeter of the square when their areas are equal.
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The paradox of tolerance admonishes us that tolerance of the intolerant leads to intolerance. The Universal Declaration of Human Rights and the constitutions and laws of Western European democracies that adhere to the principle of freedom of speech all heed the warning of this conundrum and do not afford legal protection to extremist speech. While in Western European democracies, the speech of nondemocratic extremists has been successfully outlawed, in the United States the first amendment right to freedom of speech has been interpreted to encompass radical oration. The traditional justifications of this American stance originate in the belief that speech is entitled to greater tolerance than other kinds of activity. They are based on the belief that speech itself is valuable, and thus ascribe positive value to a very broad range of speech.According to the classical model, freedom of speech serves an indispensable function in the process of democratic self-government. From this perspective, the free speech principle need only protect political speech, comprised of all the facts, theories, and opinions relating to any issue on which the citizens must vote. Proponents of this view insist that even extremist views cannot be concealed from voting citizens, if these views bear on any public issue before them.Protection of free speech serves the collective self-interests of a selfgoverning society made up of all rational, equal, and fully participating citizens who take their civic duties seriously. The fortress model is built on a foundation of pessimism, individualism, relativism, and self-doubt. At its deepest level, the fortress model values freedom of speech as a necessary precondition to the discovery and preservation of truth, but even at this level the function of speech remains primarily negative. From this perspective, the government and a majority of the people pose a great danger of intolerance. In spite of the high probability that their beliefs will eventually prove to be false, it is argued, people nonetheless tend to feel certain about them and, consequently, feel justified in requiring others to conform. Thus, the fortress models prescription for combating the tendency to censor nonconforming views is to overprotect speech by providing a broad buffer zone that encompasses extremist speech because its protection substantially diminishes the probability that inherently valuable speech will be suppressed. Directions: Read the above paragraph and answer the followingQ. All of the following actions have been put forth by one or another group in this country as being of value in our society. Which actions would violate a principle of the classical model of free speech?

If the area of an equilateral triangle is equal to the area of a square prove that the perimeter of the equilateral triangle is greater than the perimeter of the square.?
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If the area of an equilateral triangle is equal to the area of a square prove that the perimeter of the equilateral triangle is greater than the perimeter of the square.? for Verbal 2025 is part of Verbal preparation. The Question and answers have been prepared according to the Verbal exam syllabus. Information about If the area of an equilateral triangle is equal to the area of a square prove that the perimeter of the equilateral triangle is greater than the perimeter of the square.? covers all topics & solutions for Verbal 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the area of an equilateral triangle is equal to the area of a square prove that the perimeter of the equilateral triangle is greater than the perimeter of the square.?.
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