Answer:
[tex]x = 6\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex]H = 12[/tex] --Hypotenuse
Required
Calculate the unknown side length s
In a 45, 45, 90 triangle, the other side lengths are equal i.e.
Opposite = Adjacent.
Represent these side lengths with x.
Using Pythagoras theorem, we have:
[tex]Adj^2 + Opp^2 = Hyp^2[/tex]
[tex]x^2 + x^2 = 12^2[/tex]
[tex]2x^2 = 144[/tex]
Divide both sides by 2
[tex]x^2 = 72[/tex]
Take square roots of both sides
[tex]x = \sqrt{72[/tex]
Expand
[tex]x = \sqrt{36} * \sqrt{2}[/tex]
[tex]x = 6 * \sqrt{2}[/tex]
[tex]x = 6\sqrt{2}[/tex]
Hence, the other side lengths are: [tex]6\sqrt{2}[/tex]
