Answer:
[tex]\large\boxed{x=\sqrt{2.92}\ cm\approx1.71\ cm}[/tex]
Step-by-step explanation:
Look at the picture.
Segment d is the diagonal of square.
The formula of a diagonal of a square with side a:
[tex]d=a\sqrt2[/tex]
Therefore we have
[tex]a=2.4\sqrt2\ cm\to d=2.4\sqrt2\ cm[/tex]
Use the Pythagorean theorem to calculate x:
[tex]x^2+d^2=EB^2[/tex]
Substitute
[tex]d=2.4\sqrt2\ cm,\ EB=3.8\ cm[/tex]
[tex]x^2+(2.4\sqrt2)^2=(3.8)^2[/tex]
[tex]x^2+(2.4)^2(\sqrt2)^2=14.44[/tex]
[tex]x^2+(5.76)(2)=14.44[/tex]
[tex]x^2+11.52=14.44[/tex] subtract 11.52 from both sides
[tex]x^2=2.92\to x=\sqrt{2.92}\ cm\\\\x\approx1.71\ cm[/tex]
