Given $\displaystyle \Delta{A}{B}{C}$ is a right triangle with $\displaystyle \overline{{{A}{D}}}$ a perpendicular from the right angle to the hypotenuse. Give you answers as fractions of lowest terms. (Note: the picture is not to scale.)

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Find:

(i)    the length of $\displaystyle \overline{{{A}{D}}}=$

(ii)   the perimeter of $\displaystyle \Delta{A}{D}{C}=$

(iii)  the area of $\displaystyle \Delta{A}{D}{B}=$