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Ellioh · Answer 1 · 2018-02-07T16:30:29+0000

The wording is unclear without a diagram. As such, there are two possible cases and two possible answers.

Case 1: Diagonal
$\overline{DB}$ is formed by connecting the vertices formed by the meeting points of a 25-inch side and a 29-inch side.
Call the intersection point of
$\overline{DB}$ and
$\overline{AC}$ E.
$\overline{AC}$ bisects
$\overline{DB}$ , so
$DE=BE=20\text{ inches}$ . Since the diagonals of a kite are perpendicular to each other,
$\triangle AED$ and
$\triangle CED$ 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
$\overline{AC}$ , meaning
$AC=21+15=36 \text{ inches}$ , our final answer.

Case 2: Diagonal
$\overline{DB}$ is formed by connecting the vertices formed by the meeting points of the sides with equal lengths.
Call the intersection point of
$\overline{DB}$ and
$\overline{AC}$ E. We will focus on two triangles, namely
$\triangle ADE$ and
$\triangle ABE$ . 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
$\overline{AC}$ because
$\overline{DB}$ bisects
$\overline{AC}$ . Let
AE=y