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What is the perimeter of a triangle?
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The perimeter of a triangle is the sum of the lengths of its three sides.
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How do you calculate the perimeter of a triangle with side lengths 7 cm, 5 cm, and 3 cm?
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Add the side lengths: 7 + 5 + 3 = 15 cm.
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If the sides of an equilateral triangle are 10 cm each, what is its perimeter?
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The perimeter is 10 + 10 + 10 = 30 cm.
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How does the perimeter of an isosceles triangle differ if only the equal sides are given?
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Add the lengths of the two equal sides and the base: 2a + b, where a is the length of equal sides and b is the base.
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Define the perimeter of a right triangle with legs 6 cm and 8 cm, and hypotenuse 10 cm.
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The perimeter is 6 + 8 + 10 = 24 cm.
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How can knowing the perimeter of a triangle help in real-life applications?
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It can be used to determine the necessary amount of material needed to enclose or outline a triangular area.
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What is the relationship between the perimeter and the sides of a triangle?
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The perimeter is directly proportional to the sum of the side lengths of the triangle.
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Can the perimeter of a triangle be used to find the side lengths?
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Yes, but additional information is needed, such as the ratio of the sides or specific side measurements.
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Explain why the perimeter is an important geometric property.
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The perimeter determines the boundary length and is essential for understanding dimensions and scale.
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In what unit is the perimeter of a triangle measured?
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The perimeter is measured in linear units, such as centimeters, meters, or inches.
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Formulate a problem involving an isosceles triangle with a perimeter of 20 cm and one side length of 7 cm.
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Let the equal sides be x cm each. 2x + 7 = 20. Solve for x, which yields x = 6.5 cm.
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How would you calculate the perimeter of a triangle if given in algebraic form with sides a, b, and c?
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The perimeter is calculated by the expression a + b + c.
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Describe how you would find the perimeter if two sides and the area of the triangle are given.
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Use the formula for the area to find the height, then use the Pythagorean theorem if needed, or rearrange the known perimeter formula to solve for the missing side.
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Can the perimeter of a triangle provide information about its type? If yes, how?
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Yes, if the perimeter is known along with constraints on the side ratios or angles, it can help deduce whether it's equilateral, isosceles, or scalene.
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Solved example: Triangle sides are given in the ratio 3:4:5 with a perimeter of 36 cm. Find the length of each side.
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Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 36. Solving gives x = 3, so sides are 9 cm, 12 cm, and 15 cm.
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