Question

question 2 of 15, step 1 of 1
let a and b be the lengths of the legs and let c be the length of the hypotenuse of a right - triangle. using the pythagorean theorem, find the length of the side not given.
a = 12, b = 5

Explanation:

Step1: Recall Pythagorean Theorem

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

Step2: Substitute the given values

Given $a = 12$ and $b = 5$, we substitute into the formula: $c^{2}=12^{2}+5^{2}$.

Step3: Calculate the squares

$12^{2}=144$ and $5^{2}=25$, so $c^{2}=144 + 25=169$.

Step4: Solve for $c$

Taking the square root of both sides, $c=\sqrt{169}=13$.

Answer:

13