Question

what is the value of x in the right triangle shown below? 8 feet 12 feet 18 feet 23 feet

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 13$ and $a = 5$, and we want to find $b=x$. So, $x^{2}+5^{2}=13^{2}$.

Step2: Rearrange the equation

$x^{2}=13^{2}-5^{2}$. Calculate $13^{2}=169$ and $5^{2}=25$. Then $x^{2}=169 - 25=144$.

Step3: Solve for x

Take the square root of both sides. Since $x$ represents a length, we take the positive square root. $x=\sqrt{144}=12$.

Answer:

B. 12 feet