Question

find the value of x in the triangle shown below. choose 1 answer: a x = √313 b x = 1 c x = √156 d x = 5

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $c = 13$, $a = 12$ and $b=x$. So, $x^{2}+12^{2}=13^{2}$.

Step2: Rearrange the equation to solve for $x$

$x^{2}=13^{2}-12^{2}$. Calculate $13^{2}=169$ and $12^{2}=144$. Then $x^{2}=169 - 144=25$.

Step3: Find the value of $x$

Take the square - root of both sides. Since $x$ represents the length of a side of a triangle, we take the positive square root. So, $x=\sqrt{25}=5$.

Answer:

D. $x = 5$