Question

For a triangle with sides of 11, 2, and 12 is the triangle right, acute, or obtuse.

Answer 1

To determine if a triangle is right, acute, or obtuse, we can use the Pythagorean Theorem.

According to the Pythagorean Theorem, in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.

Let's square the lengths of the sides:
11^2 = 121
2^2 = 4
12^2 = 144

Now, we can compare these values:
121 + 4 = 125

Since 125 is not equal to 144, we can conclude that this triangle is not a right triangle.

In an acute triangle, the square of the length of the longest side is less than the sum of the squares of the lengths of the other two sides.

125 < 144

Therefore, this triangle is an acute triangle.