a triangle has sides of lengths 12, 14, and 19 is it a Right Triangle? Explain
To determine if a triangle is a right triangle, we need to use the Pythagorean theorem. According to the theorem, 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 other two sides.
Let's calculate the squares of the given side lengths:
12^2 = 144
14^2 = 196
19^2 = 361
Next, we will check if the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse):
144 + 196 = 340
Since 340 is not equal to 361, we can conclude that the given triangle with side lengths 12, 14, and 19 is not a right triangle.
To determine whether a triangle is a right triangle or not, we can use the Pythagorean theorem. According to the theorem, 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 other two sides.
Let's apply this to the given triangle:
- Hypotenuse: The longest side of the triangle is 19.
- Other sides: The other two sides are 12 and 14.
Now, we need to check if the Pythagorean theorem holds.
Option 1: Hypotenuse^2 = Side1^2 + Side2^2
19^2 = 12^2 + 14^2
361 = 144 + 196
361 = 340
Option 2: Side1^2 + Side2^2 = Hypotenuse^2
12^2 + 14^2 = 19^2
144 + 196 = 361
340 = 361
In both cases, we can see that the equation does not hold true. Since the values on both sides of the equation are not equal, we can conclude that the triangle with side lengths 12, 14, and 19 is not a right triangle.
So, the answer to the question is no, it is not a right triangle.
it is a right triangle only if
19^2 = 12^2 + 14^2
since
12^2 ends in 4
14^2 ends in 6
19^2 ends in 1
it is not possible.