What type of triangle has side lengths 8, 14, and 20?Group of answer choicesright triangleacute triangleobtuse trianglenot a triangleisosceles triangle

To determine the type of triangle with side lengths 8, 14, and 20, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can test this by squaring the lengths of our sides:

8^2 = 64 14^2 = 196 20^2 = 400

If this is a right triangle, then 64 + 196 should be equal to 400. Let's check:

64 + 196 = 260

Since 260 is not equal to 400, this is not a right triangle.

Next, we can check if it's an acute or obtuse triangle. In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides. In an obtuse triangle, the square of the longest side is more than the sum of the squares of the other two sides.

Since 400 (20^2) is more than 260 (8^2 + 14^2), this is an obtuse triangle.

Finally, this is not an isosceles triangle because not two sides are of equal length.

So, the answer is: this is an obtuse triangle.