The problem asks to classify triangle $EFG$ based on its side lengths and its angles. The sides have lengths 6 mm, 7 mm, and 11 mm. We need to choose two classifications from the given options.

1. Problem Description

The problem asks to classify triangle $EFG$ based on its side lengths and its angles. The sides have lengths 6 mm, 7 mm, and 11 mm. We need to choose two classifications from the given options.

2. Solution Steps

First, consider the side lengths. A scalene triangle has all sides of different lengths. Since the triangle has sides of length 6 mm, 7 mm, and 11 mm, all three sides are different. Therefore, the triangle is scalene.

Next, consider the angles. To determine if the triangle is a right triangle, obtuse, or acute, we can use the Pythagorean theorem. Let $a$, $b$, and $c$ be the side lengths, where $c$ is the longest side.

If $a^2 + b^2 = c^2$, the triangle is a right triangle.

If $a^2 + b^2 > c^2$, the triangle is an acute triangle.

If $a^2 + b^2 < c^2$, the triangle is an obtuse triangle.

Here, $a = 6$, $b = 7$, and $c = 11$.

So, $a^2 + b^2 = 6^2 + 7^2 = 36 + 49 = 85$.

And $c^2 = 11^2 = 121$.

Since $85 < 121$, we have $a^2 + b^2 < c^2$. Therefore, the triangle is an obtuse triangle.

3. Final Answer

Scalene triangle

Obtuse triangle