Question

The lengths of the diagonals of rectangle ABCD intersect at E. If AE =x+4 and CE= 3x-12. What is the length of BD?

Answer 1

Answer:

DB = 24

Step-by-step explanation:

First, note that the diagonals of a rectangle are equal and bisect each other. In other words, DB = CA and CE = EA and DE = BE.

Also, AE + CE = CA

So, using this, we can write this equation:

AE = CE

x + 4 = 3x -12

Subtract 4 from both sides.

x = 3x -16

Subtract 3x from both sides.

-2x = -16

Divide both sides by -2

x = 8

Then, substitute this into AE + CE = CA

x + 4 + 3x - 12 =

8 + 4 + 24 - 12 = 24

Then, because CA = DB,

DB = 24

I hope this helps! Feel free to ask any questions! :)

Answer 2

Step-by-step explanation:

we know that the diagonals of the rectangle are equal and bisects each other at the point of intersection.

so,

=》AE = CE

=》x + 4 = 3x - 12

=》4 + 12 = 3x - x

=》16 = 2x

=》x = 16 ÷ 2

=》x = 8

so, AE = x + 4 = 8 + 4 = 12

CE = AE = 12

now,

AC = AE + CE

=》AC = 12 + 12

=》AC = 24

and we know that diagonals of rectangle are equal so, AC = BD

hence, BD = 24