Question

find the length of the hypotenuse in the following right triangle.

13
169
10.9
17

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate \(a^{2}\) and \(b^{2}\)

$$5^{2}=25,\quad12^{2}=144$$
So \(c^{2}=25 + 144\)

Step3: Sum the values

$$c^{2}=169$$

Step4: Take the square - root

$$c=\sqrt{169}$$
Since \(c>0\) (length of a side), \(c = 13\)

Answer:

13