find the value of x. if necessary, write your answer in simplest radical form.\nx = \n(simplify your answer…

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if the hypotenuse is $c$ and the two legs are $a$ and $b$, then $c^{2}=a^{2}+b^{2}$. Here, the hypotenuse is 24 and one leg is 12, and we want to find the other leg $x$. So, $24^{2}=12^{2}+x^{2}$.

Step2: Rearrange the equation

$x^{2}=24^{2}-12^{2}$. Calculate $24^{2}=576$ and $12^{2}=144$. Then $x^{2}=576 - 144$.

Step3: Simplify the right - hand side

$x^{2}=432$.

Step4: Solve for $x$

$x=\sqrt{432}$. Factor 432: $432 = 144\times3$. So, $x=\sqrt{144\times3}$.

Step5: Use the square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 144$, $b = 3$)

$x=\sqrt{144}\cdot\sqrt{3}=12\sqrt{3}$.

Answer:

$12\sqrt{3}$