Question

Classify each triangle as acute, right or obtuse

9.6, 18, 20.1

(1 point)
These side lengths form a(n)
triangle.

Answer 1

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:

1. If \(a^2 + b^2 > c^2\), it is an acute triangle.
2. If \(a^2 + b^2 = c^2\), it is a right triangle.
3. 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 \(c^2\).

1. Calculate \(a^2\):

\[
9.6^2 = 92.16
\]

2. Calculate \(b^2\):

\[
18^2 = 324
\]

3. 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.