The answer is 13.
Because this is a kite, the diagonals intersect perpendicularly or with a 90° angle.
In the triangle DIC, which is a right triangle, the legs are 5 and 12. To find the hypotenuse, we use Pythogarean theorem:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Plug in the givens:
[tex] {5}^{2} + {12}^{2} = {c}^{2} [/tex]
Take the squares:
[tex]25 + 144 = 169 = {c}^{2} [/tex]
Take the square root of both sides:
[tex] \sqrt{169} = \sqrt{ {c}^{2} } \\ \\ c = 13[/tex]
We find the line segment DC. In the question it says "BD = DC". So BD is equal to 13.
