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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?

SOMEONE HELP ME ASAP PLEASE

The Lengths Of The Diagonals Of Rectangle ABCD Intersect At E If AE X4 And CE 3x12 What Is The Length Of BD SOMEONE HELP ME ASAP PLEASE class=

Sagot :

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! :)

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