Question

Help with geometry??

Answer 1

Answer:

A

Step-by-step explanation:

.

Answer 2

Answer:

B.) $8\sqrt{2}$

Step-by-step explanation:

Use the 45°-45°-90° theorem:

$hypotenuse=\sqrt{2}*leg$

Insert the known values:

$16=\sqrt{2}*l$

Solve for l. Divide both sides by $\sqrt{2}$ :

$\frac{16}{\sqrt{2}}=\frac{\sqrt{2}*l }{\sqrt{2} } \\\\\frac{16}{\sqrt{2} }=l\\\\l=\frac{16}{\sqrt{2} }$

Rationalize the denominator by multiplying top and bottom by the value of the denominator:

$\frac{\sqrt{2} }{\sqrt{2} } *\frac{16}{\sqrt{2}} \\\\\frac{16\sqrt{2}}{\sqrt{2}*\sqrt{2}} \\\\\frac{16\sqrt{2} }{\sqrt{4} }$

Simplify the radical:

$\frac{16\sqrt{2} }{2}$

Simplify division:

$8\sqrt{2}$

Re-insert into the equation:

$l=8\sqrt{2}$

Finito.