a triangle has a side lengths of 14 meters, 23 meters, and 25 meters.
complete the statement describing the triangle.
The triangle ______ a right triangle because_____
The triangle is a right triangle because it satisfies the condition of 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. In this case, 14^2 + 23^2 = 196 + 529 = 725, and 25^2 = 625, so the statement is:
The triangle is a right triangle because 14^2 + 23^2 = 25^2.
The triangle is a right triangle because it satisfies the Pythagorean theorem.
To determine if a triangle 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 (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have side lengths of 14 meters, 23 meters, and 25 meters. So, we can substitute these values into the Pythagorean theorem and check if it holds true.
Let's do the calculation:
(14)^2 + (23)^2 = (25)^2
196 + 529 = 625
725 = 625
The equation is not balanced, and therefore, 725 does not equal 625. Since the sides of this triangle do not satisfy the Pythagorean theorem, the triangle is NOT a right triangle.
Therefore, you can complete the statement as follows:
The triangle is NOT a right triangle because the equation (14)^2 + (23)^2 = (25)^2 does not hold true.