Mathematics, 27.01.2020 21:31 daijafoster0

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?

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Answer from: xojade

the length of the diagonal AC is 36. I just did the assignment! hope this helps

Step-by-step explanation:

Answer from: ayoismeisalex

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

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 40-x

. Using the Pythagorean Theorem, we can get the equations x^2+y^2=29^2

and

. These can simplify to x^2+y^2=841

and

. Isolating the term y^2

, we can get y^2=841-x^2

and

. The latter can simplify to y^2=-975-x^2+80x

. Using substitution, we can combine the two equations into one and get 841-x^2=-975-x^2+80x

. We can simplify that to 80x=1816

, meaning

. However, we are looking for

(

is only half of $\overline{AC}$ ). We can solve for

using the Pythagorean Theorem and the triangle with a hypotenuse of

and a leg of 22.7

. We get $y \approx 18.05$ , meaning $\overline{AC}=2y \approx 36.1 \text{ inches}$ , our final answer.

Answer from: Quest

step-by-step explanation:

The lines shown below are parallel. if the green line has a slope of 3, why is the slope of the red

Answer from: Quest

answer:

your answer is: c. 196 7/8 in^3.

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