Question

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

Answer 1

46 units

Explanation:

The diagonals of a rectangle bisect each other, which means that in this case, AE = EC. So, set the two expressions equal to each other and solve for x:

6x - 55 = 3x - 16

3x = 39

x = 13

Now, another property of rectangle diagonals is that they're the same length, which means AC = DB. So, let's just find the length of AC:

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

Thus, since AC = DB, we know that DB = 46 units.

Hope this helps!