classify a triangle with side lengths 5, 9 and 12 as acute, right, or obtuse
To determine the classification of a triangle as acute, right, or obtuse, you can use the Pythagorean theorem and compare the sum of the squares of the two shorter sides to the square of the longest side. Here's how you can do it:
Step 1: Take note of the given triangle's side lengths. In this case, the sides are 5, 9, and 12.
Step 2: Determine the longest side among the three. In this case, the longest side is 12.
Step 3: Apply the Pythagorean theorem, which states that in a right triangle, the square of the longest side (called the hypotenuse) is equal to the sum of the squares of the other two sides. In equation form, it is expressed as: a^2 + b^2 = c^2, where a and b are the two shorter sides, and c is the longest side.
Step 4: Calculate the squares of the two shorter sides. For a triangle with side lengths 5 and 9, we have:
5^2 + 9^2 = 25 + 81 = 106.
Step 5: Compare the sum of the squares of the two shorter sides to the square of the longest side. If the sum is equal to the square of the longest side, the triangle is a right triangle. If the sum is greater than the square of the longest side, the triangle is obtuse. If the sum is less than the square of the longest side, the triangle is acute.
In this case, 106 is less than 12^2 (144). Therefore, the triangle with side lengths 5, 9, and 12 is an acute triangle.