Answer:
The lenght of one leg is 22 units
Explanation:
Given
[tex]h = 22\sqrt 2[/tex] --- hypotenuse
Required
The length of one side (l)
In a 45-45-90 triangle, the two sides are equal; i.e.
[tex]x^2 + y^2 = h^2[/tex]
Where:
[tex]x = y[/tex] --- the legs of the triangle
So, we have:
[tex]x^2 + x^2 = (22\sqrt{2})^2[/tex]
[tex]2x^2 = (22\sqrt{2})^2[/tex]
This gives:
[tex]2x^2 = 968[/tex]
Divide both sides by 2
[tex]x^2 = 484[/tex]
Take square roots of both sides
[tex]x = \sqrt{484}[/tex]
[tex]x=22[/tex]
