The wording is unclear without a diagram. As such, there are two possible cases and two possible answers.
Case 1: Diagonal 
i<span><span>
s formed by connecting the vertices formed by the meeting points of a 25-inch side and a 29-inch side. </span>
</span>Call the intersection point of
and
E.
bisects
, so
. Since the diagonals of a kite are perpendicular to each other,
and
are both right triangles. One has a hypotenuse of
, and the other has a hypotenuse of
, but both share a leg of
. Using the Pythagorean Theorem, we can get that the length of the other leg in the triangle with a hypotenuse of
is
. Similarly, for the triangle with a hypotenuse of
, the other leg has a length of
. Together, these legs make up
, meaning
, our final answer.
Case 2: Diagonal i<span>
s formed by connecting the vertices formed by the meeting points of the sides with equal lengths. </span>Call the intersection point of
and
E. We will focus on two triangles, namely
and
. Since diagonals intersect perpendicularly, these triangles are right triangles. One of them has a hypotenuse of
, and the other has a hypotenuse of
. They both share a leg that is half of
because
bisects
. Let
and the non-shared leg of the right triangle with a hypotenuse of
equal
. Since
, the non-shared leg of the other right triangle (the one with a hypotenuse of
) has a length of
. Using the Pythagorean Theorem, we can get the equations
and
. These can simplify to
and
. Isolating the term
, we can get
and
. The latter can simplify to
. Using substitution, we can combine the two equations into one and get
. We can simplify that to
, meaning
. However, we are looking for
(
is only half of
). We can solve for
using the Pythagorean Theorem and the triangle with a hypotenuse of
and a leg of
. We get
, meaning
, our final answer.
