Answer: The length of AD is 22 units.
Step-by-step explanation: Given that the quadrilateral ABCD in the figure is a kite. Also, AD is congruent to AB.
We are to find the length of AD.
Also, given in the figure that
AD = 2r + 8 and AB = 5r - 13.
A KITE is a quadrilateral having congruent adjacent sides and the diagonals bisect each other perpendicularly.
Since ABCD is a kite and side AD is adjacent to side AB.
Therefore, we must have
[tex]AD=AB\\\\\Rightarrow 2r+8=5r-13\\\\\Rightarrow 5r-2r=8+13\\\\\Rightarrow 3r=21\\\\\Rightarrow r=7.[/tex]
So, the length of AD is given by
[tex]AD=2r+8=2\times 7+8=14+8=22.[/tex]
Thus, the length of AD is 22 units.
