Can a right triangle have sides of length 1, 7, and 5 to the square root of 2? Justify your answer.
can a^2 + b^2 = c^2
????
Thank you!
To determine whether a triangle is a right triangle, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side. This is known as the Pythagorean theorem.
In this case, the lengths of the sides are 1, 7, and 5√2. Let's calculate the squares of these lengths:
1^2 = 1
7^2 = 49
(5√2)^2 = 50
The sum of the squares of the two shorter sides (1 and 49) is 50, which is equal to the square of the longest side (50). Therefore, according to the Pythagorean theorem, this triangle is a right triangle.
To check if a triangle is a right triangle, we can use the Pythagorean theorem:
If a^2 + b^2 = c^2, where 'a', 'b', and 'c' represent the lengths of the sides of the triangle, then the triangle is a right triangle.