Solution
To solve this question, we will apply Pythagoras theorem, which states that:
[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]- We are given that:
[tex]\begin{gathered} Hypotenuse=3 \\ Opposite=Adjacent=x \end{gathered}[/tex]- Thus, we can say:
[tex]\begin{gathered} 3^2=x^2+x^2 \\ 2x^2=9 \\ \text{ Divide both sides by 2} \\ x^2=\frac{9}{2} \\ \\ Take\text{ the square root of both sides} \\ x=\sqrt{\frac{9}{2}}=\frac{3}{\sqrt{2}} \\ \\ x=\frac{3}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}} \\ \\ x=\frac{3}{2}\sqrt{2} \end{gathered}[/tex]Final Answer
The length of the legs are:
[tex]\frac{3}{2}\sqrt{2}[/tex]