If AE=6x-55 and EC=3x-16, find DB. (Hint: Find x first and then substitute.)

Answer:

46 units

Step-by-step explanation:

The diagonals of a rectangle intersect at their midpoints, indicating AE = EC. Therefore, set the equations equal and solve for x:

6x - 55 = 3x - 16

3x = 39

x = 13

Additionally, another characteristic of rectangle diagonals is their equal lengths, hence AC = DB. Now, let’s assess the length of AC:

AC = AE + EC = (6 * 13 - 55) + (3 * 13 - 16) = 23 + 23 = 46

Since AC = DB, it follows that DB = 46 units.

I hope this clarifies your question!