Question

Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?

Answer 1

Use the Pythagorean theorem:
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\ 6^2+6^2=x^2 \\ 6^2 \times 2=x^2 \\ \sqrt{6^2 \times 2}=x \\ \sqrt{6^2} \times \sqrt{2}=x \\ 6\sqrt{2}=x$
 
The length of the hypotenuse is 6√2 units.