#### Answer

$x$=$\frac{5\sqrt 2}{2}$

#### Work Step by Step

Step 1: The formula to be used is $H^{2}=B^{2}+P^{2}$
where H,B and P represent Hypotenouse, Base and Perpendicular respectively
Step 2: According to the figure, H=5, B=x and P=x
Step 3: Substituting these values into the formula, $5^{2}=x^{2}+x^{2}$
Step 4: $5^{2}=2x^{2}$
Step 5: $\frac{5^{2}}{2}=x^{2}$
Step 6: Taking square root on both sides, $\frac{5}{\sqrt 2}$ =$x$
Step 7: Multiplying both numerator and denominator of the left side by $\sqrt 2$, we get $\frac{5\sqrt 2}{2}$ =$x$
Step 8: Therefore, $x$=$\frac{5\sqrt 2}{2}$