a triangle has sides with lengths of 11 meters, 9 meters, and 7 meters. what type of triangle is it?
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In a scalene triangle, all sides are unequal.
To determine the type of triangle based on side lengths, we need to classify it based on the relationships between the sides. Here are the steps:
Step 1: Identify the longest side:
Out of the three given side lengths, 11 meters is the longest side.
Step 2: Apply the Triangle Inequality Theorem:
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this condition is satisfied for the given triangle:
- 11 + 9 = 20 (greater than 7)
- 11 + 7 = 18 (greater than 9)
- 9 + 7 = 16 (greater than 11)
Since all three conditions are satisfied, we can conclude that the given side lengths can form a triangle.
Step 3: Identify the type of triangle:
Based on the given side lengths, we can classify the triangle as follows:
- A triangle with side lengths of 11 meters, 9 meters, and 7 meters is a Scalene triangle.
- Since all three sides have different lengths, none of the angles are equal either.
So, the given triangle is a Scalene triangle.
To determine the type of triangle, you need to consider the lengths of its sides. In this case, the triangle has sides measuring 11 meters, 9 meters, and 7 meters.
To identify the type of triangle, we can apply some basic principles:
1. If all three sides have the same length, it is an equilateral triangle.
2. If any two sides have the same length, it is an isosceles triangle.
3. If all three sides have different lengths, it is a scalene triangle.
Let's apply these principles to your given triangle:
- The sides of lengths 11 meters, 9 meters, and 7 meters are all different, so it is not an equilateral triangle.
- None of the sides have the same length, so it is not an isosceles triangle.
Hence, based on the given side lengths, the triangle can be classified as a scalene triangle.