Question

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?

inches

Answer 1

To find the length of diagonal AC, you can use the Pythagorean theorem to first find the length of diagonal DB. Then, since the diagonals of a kite intersect at right angles, you can use the Pythagorean theorem again to find the length of diagonal AC.

Step-by-step explanation:

To find the length of diagonal AC, we can use the Pythagorean theorem. Since we know the lengths of the top and bottom sides of the sandbox, we can calculate the length of the diagonal DB using the Pythagorean theorem:

DB^2 = 29^2 + 25^2

DB^2 = 841 + 625

DB^2 = 1466

DB = √1466 = 38.28 (approx.)

Now, to find the length of diagonal AC, we can use the fact that the diagonals of a kite intersect at right angles. Therefore, we have two right triangles, ADB and ADC, where the diagonals are the hypotenuses. Using the Pythagorean theorem again:

AC^2 = AD^2 + DC^2

AC^2 = (DB/2)^2 + (DB/2)^2

AC^2 = (38.28/2)^2 + (38.28/2)^2

AC^2 = 19.14^2 + 19.14^2

AC^2 = 366.99 + 366.99

AC^2 = 733.98

AC = √733.98 = 27.07 (approx.)

Answer 2

the answer is 36 i took the test