## Algebra: A Combined Approach (4th Edition)

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