Mathematics: Kara is building a sandbox shaped like a kite for her nephew. the top two sides of the sandbox are 29 inches long. the bottom two sides are 25 inches long. the diagonal db has a length of 40 inches. what is the length of the diagonal ac?

3,3,6Step-by-step explanation:...

Kara is building a sandbox shaped like a kite

Ответ:

zarrialamons16

16.01.2022

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

. 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