Answer:
c = 3[tex]\sqrt{6}[/tex]
Step-by-step explanation:
triangle is right isosceles so both sides equal 3[tex]\sqrt{3}[/tex]
can use pythagorean theorem which is square each leg and set it equal to the hypotenuse (side 'c') squared
(3[tex]\sqrt{3}[/tex])^2 + (3[tex]\sqrt{3}[/tex])^2 = c^2
(9x3) + (9x3) = c^2
27 + 27 = c^2
54 = c^2
c = [tex]\sqrt{54}[/tex]
simplify [tex]\sqrt{54}[/tex] to equal = [tex]\sqrt{9}[/tex] x [tex]\sqrt{6}[/tex] which simplies to 3[tex]\sqrt{6}[/tex]
