Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\). For a \(45 - 45-90\) triangle, \(a = b=x\).
So, \(x^{2}+x^{2}=c^{2}\).

Step2: Simplify the equation

\(2x^{2}=c^{2}\).
Take the square root of both sides: \(c=\sqrt{2x^{2}}\).
Since \(x\gt0\) (length), \(c = x\sqrt{2}\).

Answer:

\(x\sqrt{2}\)