QuestionWhich best describes the triangle or triangles, if any, that can be formed with sides measuring 60 centimeters, 100 centimeters, and 40 centimeters? two unique scalene triangles no triangle one unique scalene triangle infinitely many similar scalene triangles
Studdy Solution
STEP 1
1. To determine if a triangle can be formed with given side lengths, we need to use the triangle inequality theorem.
2. The triangle inequality theorem states that for any three sides to form a triangle, the sum of any two sides must be greater than the third side.
3. If the side lengths meet the triangle inequality conditions, we will then classify the triangle based on its side lengths.
STEP 2
1. Verify the triangle inequality theorem for the given side lengths.
2. Determine if the side lengths form a triangle.
3. Classify the type of triangle formed, if any.
STEP 3
Check the triangle inequality theorem condition involving the sides 60 cm, 100 cm, and 40 cm:
STEP 4
Calculate: Since , the first condition fails.
STEP 5
Since the first condition fails, it is not necessary to check the remaining conditions. The sides do not satisfy the triangle inequality theorem. Therefore, a triangle cannot be formed.
STEP 6
Since the sides do not satisfy the triangle inequality theorem, no triangle can be formed with sides measuring 60 cm, 100 cm, and 40 cm.
STEP 7
There is no need to classify the triangle as no triangle can be formed.
Solution:
No triangle can be formed with the given side lengths.
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