Question

each leg of a 45 - 45 - 90 triangle has a length of 6 units. what is the length of its hypotenuse?
a. 6\sqrt{2} units
b. 12 units
c. 3\sqrt{2} units
d. 6 units

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In a 45 - 45 - 90 triangle, \(a = b=6\).

Step2: Substitute values into the formula

Substitute \(a = 6\) and \(b = 6\) into \(a^{2}+b^{2}=c^{2}\), we get \(6^{2}+6^{2}=c^{2}\), which is \(36 + 36=c^{2}\), so \(c^{2}=72\).

Step3: Solve for \(c\)

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

Answer:

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