Question

question 8 of 25 each leg of a 45 - 45 - 90 triangle has a length of 6 units. what is the length of its hypotenuse? a. 3√2 units b. 12 units c. 6 units d. 6√2 units

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs.

Step2: Substitute leg lengths

For a 45 - 45 - 90 triangle with \(a = b=6\), we have \(c^{2}=6^{2}+6^{2}\).
\[

$$\begin{align*} c^{2}&=36 + 36\\ c^{2}&=72 \end{align*}$$

\]

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{72}\). Simplify \(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\).

Answer:

D. \(6\sqrt{2}\) units