if a triangle has sides 12, 16, and 20, which length is the length of the hypotenuse
In a right triangle, the hypotenuse is the side that is opposite the right angle. If a triangle has sides of 12, 16, and 20 units, there is a possibility that it is a right triangle with sides 12 and 16 forming the legs and side 20 as the hypotenuse.
To confirm this, 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 lengths of the other two sides.
Using this theorem, we can check if 12² + 16² = 20²:
12² + 16² = 144 + 256 = 400
20² = 400
Since both sides of the equation are equal, we can conclude that the triangle with side lengths 12, 16, and 20 is indeed a right triangle. Therefore, the length of the hypotenuse is 20 units.