Answer:
B.) [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Use the 45°-45°-90° theorem:
[tex]hypotenuse=\sqrt{2}*leg[/tex]
Insert the known values:
[tex]16=\sqrt{2}*l[/tex]
Solve for l. Divide both sides by [tex]\sqrt{2}[/tex] :
[tex]\frac{16}{\sqrt{2}}=\frac{\sqrt{2}*l }{\sqrt{2} } \\\\\frac{16}{\sqrt{2} }=l\\\\l=\frac{16}{\sqrt{2} }[/tex]
Rationalize the denominator by multiplying top and bottom by the value of the denominator:
[tex]\frac{\sqrt{2} }{\sqrt{2} } *\frac{16}{\sqrt{2}} \\\\\frac{16\sqrt{2}}{\sqrt{2}*\sqrt{2}} \\\\\frac{16\sqrt{2} }{\sqrt{4} }[/tex]
Simplify the radical:
[tex]\frac{16\sqrt{2} }{2}[/tex]
Simplify division:
[tex]8\sqrt{2}[/tex]
Re-insert into the equation:
[tex]l=8\sqrt{2}[/tex]
Finito.
