Question

Quadrilateral ABCD is a kite. If , AD is congruent to AB find AD.

Answer 1

AD = AB
2r + 8 = 5r - 13
3r = 21
r = 7

AD = 2r + 8 = 2(7) + 8 = 14 + 8 = 22

answer AD = 22

Answer 2

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

$AD=AB\\\\\Rightarrow 2r+8=5r-13\\\\\Rightarrow 5r-2r=8+13\\\\\Rightarrow 3r=21\\\\\Rightarrow r=7.$

So, the length of AD is given by

$AD=2r+8=2\times 7+8=14+8=22.$

Thus, the length of AD is 22 units.