Question

The sides of a triangle have lengths 2, 6, and 7. What kind of triangle is it?

Answer 1

an obtuse triangle.

Explanation:

To determine the type of triangle with sides of lengths 2, 6, and 7, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we can check whether this condition holds for the three sides of lengths 2, 6, and 7:

2 + 6 > 7 (True)

6 + 7 > 2 (True)

2 + 7 > 6 (True)

Since all three inequalities are true, the given lengths of 2, 6, and 7 form a valid triangle.

To determine the type of triangle, we can use the lengths of the sides and the Pythagorean theorem or trigonometric functions. For this triangle, we can use the Pythagorean theorem to find that the longest side (7) is opposite the largest angle, which is greater than 90 degrees. Therefore, this triangle is an obtuse triangle.

Answer 2

Scalene triangle

Explanation:

To determine the type of triangle, we need to compare the lengths of the sides to each other.

If all three sides have the same length, it's an equilateral triangle.

If two sides have the same length and the third is different, it's an isosceles triangle.

If all three sides have different lengths, it's a scalene triangle.

Using the lengths given, we see that all three sides have different lengths, so this is a scalene triangle.