Tell whether the triangle with the given side is a right triangle;14mm, 19mm, 23mm
It's not a right triangle.
thank you this is very helpful
To determine whether the triangle with side lengths 14mm, 19mm, and 23mm is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's check if this condition is satisfied for the given triangle:
14^2 + 19^2 = 196 + 361 = 557
23^2 = 529
Since 557 is not equal to 529, we can conclude that the triangle with side lengths 14mm, 19mm, and 23mm is not a right triangle.
To determine if a triangle is a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem 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.
Let's apply this theorem to the given triangle with sides measuring 14mm, 19mm, and 23mm.
Step 1: Arrange the sides in ascending order. In this case, it would be 14mm, 19mm, 23mm.
Step 2: Apply the Pythagorean theorem: If a^2 + b^2 = c^2, where 'a' and 'b' are the shorter sides and 'c' is the hypotenuse, it is a right triangle.
In this case, 14^2 + 19^2 = 196 + 361 = 557.
23^2 = 529.
Step 3: Compare the two values obtained in Step 2: 557 and 529.
Since 557 is not equal to 529, the triangle does not satisfy the Pythagorean theorem. Therefore, the given triangle with side lengths of 14mm, 19mm, and 23mm is not a right triangle.