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Let's break this down step by step.

We are asked to compute the squares of certain sides of a triangle with side lengths of 18, 15, and 6, and determine the type of triangle.

### 1. Compute the sum of the squares of the shorter sides:
The shorter sides are 6 and 15.

\[
6^2 + 15^2 = 36 + 225 = 261
\]

So, the sum of the squares of the shorter sides is **261**.

### 2. Compute the square of the longest side:
The longest side is 18.

\[
18^2 = 324
\]

### 3. Determine the type of triangle:
To determine the type of triangle, we compare the sum of the squares of the shorter sides to the square of the longest side:
- If \( a^2 + b^2 = c^2 \), it's a **right triangle**.
- If \( a^2 + b^2 > c^2 \), it's an **acute triangle**.
- If \( a^2 + b^2 < c^2 \), it's an **obtuse triangle**.

In this case, \( 261 < 324 \), meaning the triangle is an **obtuse triangle**.

Would you like further details or have any questions?

### Related Questions:
1. What is the Pythagorean Theorem, and how is it applied?
2. How do we classify triangles based on their angles?
3. Can a triangle have more than one obtuse angle?
4. What happens if all three sides of a triangle are equal?
5. How do you calculate the area of a triangle given the side lengths?

### Tip:
Whenever comparing the squares of a triangle's sides, remember that the relationship between them helps you classify the triangle as right, acute, or obtuse.

The other triangle has side lengths 18, 15, and 6. Compute the sum of the squares of the shorter lengths and the square of the longest length. What kind of triangle is it?

Learn how to classify a triangle with side lengths 18, 15, and 6 by calculating the squares of its sides and applying the Pythagorean theorem. Suitable for students in Grades 8-10.

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