Question

what does the pythagorean theorem say about the side lengths of this triangle? pythagorean theorem triangle with legs a, b and hypotenuse c options: $a^2 + c^2 = b^2$, $a^2 + b^2 = c^2$, $a^2 - b^2 = c^2$, $(a + b)^2 = c^2$

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem 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 the given right - triangle, the hypotenuse is \(c\) (as it is opposite the right angle), and the other two sides are \(a\) and \(b\).

Step2: Apply the Theorem

According to the Pythagorean Theorem, if the lengths of the two legs (the sides forming the right angle) are \(a\) and \(b\), and the length of the hypotenuse is \(c\), then the relationship between the side lengths is \(a^{2}+b^{2}=c^{2}\).

Answer:

\(a^{2}+b^{2}=c^{2}\) (the option with this formula)