Question

writing find the length of the hypotenuse of the right triangle. use pencil and paper. explain how you can interpret the pythagorean theorem using the areas of squares. (the figure is not drawn to scale.) the length of the hypotenuse is \\(\square\\) (simplify your answer)

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle with legs \(a = 14\) and \(b = 48\), and hypotenuse \(c\), the Pythagorean Theorem states \(a^{2}+b^{2}=c^{2}\).
\[

$$\begin{align*} 14^{2}+48^{2}&=c^{2}\\ 196 + 2304&=c^{2}\\ 2500&=c^{2} \end{align*}$$

\]

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{2500} = 50\).

Answer:

50