Question

based on the measurements in the diagram, what is k? a. 8 ft. b. 11 ft. c. 12 ft. d. 18 ft.

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Rearrange the formula to solve for $k$

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

Step3: Find the value of $k$

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

Answer:

C. 12 ft.