Answer:
[tex]\text{The hypotenuse of a }45^\circ\text{ - }45^\circ\text{ - }90^\circ\text{ triangle is equal to a leg }\boxed{\text{multiplied}}\text{ by }\\\boxed{\sqrt2}\ .[/tex]
Step-by-step explanation:
[tex]\text{By the pythagoras theorem, the hypotenuse of the triangle is given by: }\\\\h=\sqrt{\big(\sqrt5\big)^2+\big(\sqrt5\big)^2}=\sqrt{5+5}=\sqrt{10}=\sqrt{5\times2}=\sqrt{5}\times\sqrt2\\\\\text{i.e. hypotenuse = a leg }\times\sqrt2[/tex]
[tex]\text{Remember, the concept I used here in the second last and last step, }\\\\\sqrt {ab}=\sqrt a\times\sqrt b\text{ is not applicable if both }a\text{ and }b\text{ are negative numbers.}[/tex]
