Question

The lengths of the sides of a triangle are 4​, 6​, and 8. Classify the triangle as​ acute, right, or obtuse.
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Part 1
Choose the correct type of triangle below.

Answer 1

To classify the triangle with side lengths 4, 6, and 8, we can use the property that relates the sides of a triangle to determine whether it is acute, right, or obtuse.

Let \(a = 4\), \(b = 6\), and \(c = 8\) (where \(c\) is the longest side).

1. Calculate \(a^2 + b^2\):
\[
a^2 + b^2 = 4^2 + 6^2 = 16 + 36 = 52
\]

2. Calculate \(c^2\):
\[
c^2 = 8^2 = 64
\]

Now, we will compare \(a^2 + b^2\) and \(c^2\):

- If \(a^2 + b^2 > c^2\), the triangle is acute.
- If \(a^2 + b^2 = c^2\), the triangle is right.
- If \(a^2 + b^2 < c^2\), the triangle is obtuse.

In this case:
\[
52 < 64
\]

Since \(a^2 + b^2 < c^2\), the triangle is classified as **obtuse**.