Question

what does c = √65 mean in this problem? a = 7 a² + b² = c² 7² + 4² = c² 49 + 16 = c² 65 = c² √65 = c c = √65 b = 4 the length of is √65. one of the legs the hypotenuse

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse.

Step2: Analyze given values

Given $a = 7$ and $b = 4$, we calculate $a^{2}+b^{2}=7^{2}+4^{2}=49 + 16=65$. Then $c^{2}=65$, so $c=\sqrt{65}$. Since $c$ is the side opposite the right - angle, it is the hypotenuse.

Answer:

the hypotenuse