To classify the triangle based on its side lengths, we can use the Pythagorean theorem. For a triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), we can determine the type of triangle as follows:
- If \(a^2 + b^2 > c^2\), it is an acute triangle.
- If \(a^2 + b^2 = c^2\), it is a right triangle.
- If \(a^2 + b^2 < c^2\), it is an obtuse triangle.
Given the sides \(9.6\), \(18\), and \(20.1\), we identify \(20.1\) as the longest side, so we have:
- \(a = 9.6\)
- \(b = 18\)
- \(c = 20.1\)
Now, we calculate \(a^2 + b^2\) and compare it to \(c^2\).
- Calculate \(a^2\):
\[ 9.6^2 = 92.16 \]
- Calculate \(b^2\):
\[ 18^2 = 324 \]
- Calculate \(c^2\):
\[ 20.1^2 = 404.01 \]
Now, add \(a^2\) and \(b^2\) together:
\[ a^2 + b^2 = 92.16 + 324 = 416.16 \]
Now we compare \(a^2 + b^2\) to \(c^2\):
\[ 416.16 > 404.01 \]
Since \(a^2 + b^2 > c^2\), the triangle is classified as an acute triangle.
Thus, these side lengths form an acute triangle.
1 answer