Question

what is the length of the hypotenuse of a 45 - 45 - 90? * 1 point
x
$x\sqrt{2}$
$x\sqrt{3}$
$2x$

Explanation:

Step1: Apply Pythagorean theorem

Let the legs of the 45 - 45 - 90 triangle be of length \(x\). By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = x\), \(b = x\), and \(c\) is the hypotenuse.
So, \(x^{2}+x^{2}=c^{2}\).

Step2: Simplify the equation

\(2x^{2}=c^{2}\). Then \(c=\sqrt{2x^{2}}\).
Since \(x>0\) (length), \(c = x\sqrt{2}\).

Answer:

\(x\sqrt{2}\)