How to find the perimeter of an isosceles triangle?
Understand the Problem
The question is asking for a method to calculate the perimeter of an isosceles triangle, which is based on the lengths of its sides. To find the perimeter, we need to sum the lengths of all three sides of the triangle.
Answer
The perimeter is given by \( P = 2a + b \).
Answer for screen readers
The perimeter of the isosceles triangle is given by the formula ( P = 2a + b ).
Steps to Solve
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Identify the Side Lengths Determine the lengths of the two equal sides and the base of the isosceles triangle. Let's denote the lengths of the two equal sides as $a$ and the length of the base as $b$.
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Set Up the Perimeter Formula The formula for the perimeter $P$ of a triangle is the sum of the lengths of its sides. For an isosceles triangle, the perimeter can be represented as: $$ P = a + a + b $$
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Simplify the Perimeter Formula Combine the two equal sides in the formula: $$ P = 2a + b $$
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Substitute Known Values If you have specific values for $a$ and $b$, substitute these values into the formula. For example, if $a = 5$ and $b = 8$, then: $$ P = 2(5) + 8 $$
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Calculate the Perimeter Perform the arithmetic to find the perimeter: $$ P = 10 + 8 = 18 $$
The perimeter of the isosceles triangle is given by the formula ( P = 2a + b ).
More Information
The perimeter of an isosceles triangle helps in various applications, such as designing and constructing structures or understanding geometric principles in mathematics.
Tips
A common mistake is forgetting to add both equal sides together or confusing the lengths of sides. To avoid this, always double-check that you are adding both equal sides as $2a$.
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