a triangle has side lengths of 12 cm, 15 cm and 20 cm. Classify it as acute obtuse or right
To classify the triangle as acute, obtuse, or right, we need to determine the type of angles formed by the triangle.
1. To check if it is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
If a^2 + b^2 = c^2 (where c is the longest side or hypotenuse), then it is a right triangle.
2. If a^2 + b^2 < c^2, then it is an obtuse triangle.
If a^2 + b^2 > c^2, then it is an acute triangle.
Given the side lengths of 12 cm, 15 cm, and 20 cm, let's determine the type of triangle:
Using the Pythagorean theorem:
12^2 + 15^2 = 144 + 225 = 369
20^2 = 400
Since 369 is less than 400, it means 12 cm, 15 cm, and 20 cm do not form a right triangle.
Therefore, we need to compare the sum of the squares of the two smaller sides (12^2 + 15^2 = 369) with the square of the longest side (20^2 = 400). Since 369 is less than 400, it indicates that the angles of this triangle are all acute.
Therefore, the triangle with side lengths of 12 cm, 15 cm, and 20 cm is classified as an acute triangle.