Answer:
[tex]x=4\sqrt{2}\ cm[/tex]
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides
Let
x ----> the length of the leg
Applying the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
where
c is the hypotenuse (the greater side)
a and b are the legs of the right triangle
In this problem we have
[tex]c=8\ cm[/tex]
[tex]a=b=x\ cm[/tex]
substitute
[tex]8^2=x^2+x^2\\\\64=2x^2\\\\x^2=32\\\\x=\sqrt{32}\ cm[/tex]
simplify
[tex]x=4\sqrt{2}\ cm[/tex]
