00:24:00
KCKC-213
perimeter of a triangle.
To find the perimeter of a triangle, you need to add the lengths of all its sides. There are different cases to consider based on the given information:
### 1. If All Three Sides of the Triangle Are Given:
If you know the lengths of all three sides of the triangle, simply add them together to find the perimeter.
[ ext{Perimeter} = a + b + c ]
where (a), (b), and (c) are the lengths of the three sides.
### 2. If Given Two Sides and an Included Angle (SSS Triangle):
If two sides and the included angle are known, you can use the Law of Cosines to find the third side, then sum all sides to find the perimeter.
[ c^2 = a^2 + b^2 - 2abcos(gamma) ]
[ c = sqrt{a^2 + b^ - 2abcos(gamma)} ]
[ ext{Perimeter} = a + b + c ]
### 3. If Given Two Sides and an Inscribed Angle (SAS Triangle):
If two sides and the non-included angle are given, you can use the Law of Sines to find the third side, then sum all sides to find the perimeter.
[ frac{a}{sin(alpha)} = frac{b}{sin(eta)} = frac{c}{sin(gamma)} ]
[ ext{Perimeter} = a + b + c ]
### 4. If Given Two Angles and a Side (ASA Triangle):
If two angles and the included side are known, you can find the third angle and then use the Law of Sines to find the remaining sides, then sum all sides to find the perimeter.
[ ext{Perimeter} = a + b + c ]
### 5. If Given a Right Triangle:
If the triangle is right, use the Pythagorean Theorem to find the unknown side, then sum all sides to find the perimeter.
[ ext{Perimeter} = a + b + c ]
### 6. If Given an Equilateral Triangle:
If the triangle is equilateral, the perimeter is three times one side.
[ ext{Perimeter} = 3a ]
### 7. If Given an Isosceles Triangle:
If the triangle is isosceles, add the lengths of all sides.
[ ext{Perimeter} = 2b + c ]
### 8. If Given the Sides of a Scalene Triangle:
If the triangle is scalene, add the lengths of all sides.
[ ext{Perimeter} = a + b + c ]
### 9. If Given a Triangle with One Side:
If one side of the triangle is given, you can find the other sides using trigonometry or other methods, then sum all sides to find the perimeter.
[ ext{Perimeter} = a + b + c ]
### 10. If Given an Asymptote Triangle:
If the triangle is asymptotic, you can find the perimeter by adding the lengths of the sides.
[ ext{Perimeter} = a + b + c ]
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31 Jan 2025
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