To classify a triangle based on the given side lengths (26, 12, and 18), we can use the triangle inequality theorem and properties of different types of triangles. Here, we're focusing on whether the triangle is acute, obtuse, or right.
1. **First, verify if the sides form a triangle** using the triangle inequality theorem:
- The sum of the lengths of any two sides must be greater than the length of the remaining side.
- \(26 + 12 > 18 \quad \text{(38 > 18)}\)
- \(26 + 18 > 12 \quad \text{(44 > 12)}\)
- \(12 + 18 > 26 \quad \text{(30 > 26)}\)
All these conditions are satisfied, so these sides do form a triangle.
2. **Next, determine the type of triangle** using the Pythagorean theorem for right triangles:
- For a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) should be equal to the sum of the squares of the other two sides.
- Here, the longest side is 26.
- Check if \(26^2\) is equal to \(12^2 + 18^2\):
- \(26^2 = 676\)
- \(12^2 = 144\)
- \(18^2 = 324\)
- \(144 + 324 = 468\)
Since \(676 \neq 468\), the triangle is not a right triangle.
3. **Determine if the triangle is acute or obtuse**:
- For an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.
- For an obtuse triangle, the square of the longest side is more than the sum of the squares of the other two sides.
- We already have \(676 \text{ (}26^2\text{)} \) and \(468 \text{ (}12^2 + 18^2\text{)}\).
Since \(676 > 468\), the triangle is obtuse.
So, the triangle with side lengths 26, 12, and 18 is **obtuse**.
Classify a triangle with the following side lengths 26, 12, and 18.
*
Acute
Obtuse
Right
1 answer