Question

Figure ABCD is a rectangle. The length of segment AE is (4x – 3) units and the length of segment EC is (x + 3) units.

Rectangle ABCD with point E as the point of intersection of the two diagonals. The length of AE is labeled (4x – 3) and the length of EC is labeled (x + 3).

What is the length of diagonal BD?

Answer 1

The diagonals of a rectangle are congruent, which means the length of BD = the length of AC. Also, the diagonals of a rectangle bisect each other. That means AE = EC.

Answer 2

so what do i do

Answer 3

You set AE = CE which means 4x - 3 = x + 3
Solve that equation for x.

Answer 4

4x - 3 = x + 3
Subtract x from both sides
3x - 3 = 3
Add 3 to both sides
3x = 6
x = 2
Now with x = 2, how long is AC:
AC = AE + EC
AC = 4x - 3 + x + 3
but x = 2, so
AC = 4(2) - 3 + 2 + 3 = 8 - 3 + 2 + 3 = 10
Sice AC = 10 and we know that BD = AC, then BD = 10