Question

in the triangle shown below, what is the approximate value of x? a. 18 units b. 20.78 units c. 26.83 units d. 12 units

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $a = 12$, $c = 24$, and we need to find $b=x$. So, $x=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 12$ and $c = 24$ into the formula: $x=\sqrt{24^{2}-12^{2}}=\sqrt{(24 + 12)(24 - 12)}$ (using $a^{2}-b^{2}=(a + b)(a - b)$). Then $x=\sqrt{36\times12}=\sqrt{432}$.

Step3: Calculate the square - root

$\sqrt{432}\approx20.78$.

Answer:

B. 20.78 units