Question

A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Classify it as acute, obtuse, or right

acute

obtuse

right

Answer 1

To classify the triangle with sides 18 cm, 80 cm, and 81 cm, we can use the properties of triangles and the Pythagorean theorem.

First, we will identify the longest side, which is 81 cm. We will denote the sides as follows:
- \( a = 18 \) cm
- \( b = 80 \) cm
- \( c = 81 \) cm (the longest side)

According to the classification based on the side lengths:
- If \( c^2 < a^2 + b^2 \), the triangle is acute.
- If \( c^2 = a^2 + b^2 \), the triangle is right.
- If \( c^2 > a^2 + b^2 \), the triangle is obtuse.

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

1. Calculate \( c^2 \):
\[
c^2 = 81^2 = 6561
\]

2. Calculate \( a^2 + b^2 \):
\[
a^2 = 18^2 = 324
\]
\[
b^2 = 80^2 = 6400
\]
\[
a^2 + b^2 = 324 + 6400 = 6724
\]

Now, we can compare \( c^2 \) with \( a^2 + b^2 \):
- \( c^2 = 6561 \)
- \( a^2 + b^2 = 6724 \)

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