Question

find the side length of x. right triangle with legs 5 mi and x, hypotenuse 13 mi. options: 18, 8, 12, 25

Explanation:

Step1: Apply Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, substitute $a=5$, $c=13$, $b=x$
$5^2 + x^2 = 13^2$

Step2: Calculate squared values

Compute $5^2$ and $13^2$
$25 + x^2 = 169$

Step3: Isolate $x^2$

Subtract 25 from both sides
$x^2 = 169 - 25 = 144$

Step4: Solve for $x$

Take square root of 144
$x = \sqrt{144}$

Answer:

12