Question

The sum of the lengths of the diagonals of a rhombus is 22, AE is 2x + 1, BE is x - 2. What is the length of BD?

Answer 1

omg is this geometry??

Answer 2

yes?

Answer 3

then.............

Answer 4

?

Answer 5

i can't help you sorry but ask ash2326

Answer 6

-.-

Answer 7

I don't know how yo use this site to find ash2326 :(

Answer 8

ok so diagonal AD is 4x+2 and diagonal BC is 2x-4. The sum of the lengths of the diagonals is 22, so AD+BC is 4x+2+2x-4=22
so 6x-2 = 22 -> 6x = 24 -> x = 4.
You plug that in for the lengths of half the diagonals 2(4) +1 = 9 and
4-2 = 2. So then you just put a^2 + b^2 = c^2 to find side c which is side BD.
The opposite sides of a rhombus are equal to each other,
so you just need to find one outside length.

Answer 9

AE is 2x + 1
then AD= 2(2x+1)
BE is x - 2
then BC= 2(x-2)

Answer 10

so is AD the c^2?

Answer 11

wait what???

Answer 12

BD = C

Answer 13

so 2^2+9^2=c^2???

Answer 14

yes off-course

Answer 15

so then 4+ 81=c^2
85=c^2
square root 85=9.2
but 9.2 isn't an answer???

Answer 16

lemme check

Answer 17

yap correct

Answer 18

but 9.2 isn't an answer so its wrong?

Answer 19

wait lemme check

Answer 20

Wait, back it up. There's no need to use the pythagorean theorem. If you know what x is (which annas figured out) then you can plug it in and find out how long BE is. And then you can double it to find out how long BD is. You'd only use the pythagorean theorem to figure out how long the sides of the rhombus are, but the problem isn't asking about that.

Answer 21

what do you plug x into though???

Answer 22

exactly i forgot to double the value 9.2 is half length 2*9.2 is BD 18.4

Answer 23

The diagonals add up to 22.

So 2x + 1 + 2x + 1 + x - 2 + x - 2 = 22

You solve for x, then that's the value you plug in.

Answer 24

@annas: You don't need outside lengths at all. 9.2 has nothing to do with the problem.

Answer 25

ok :) i can also be wrong as i m human. could you please explain the rest
thanks for correcting me

Answer 26

okay we got x which =4 I plugged it in and yes it does =22
now I still don't know how to get BD?
4,8,12, and 16 is what I can choose from.
Or is x just the answer for BD and the answer is 4?

Answer 27

BE = x-2
First, figure out how long BE is.
Then realize that BD is just twice as long.

Answer 28

x=4
so BE=x-2
(4)-2=2
2+2=4
so the answer is 4? right? :)

Answer 29

Yes. Good.
The fact that x is 4 and the answer is 4 is complete coincidence, by the way. They don't always have to be the same...they just are in this case.

Answer 30

OMGSHH ! thankyouuu SO SO SO SO SO SO MUCH! both of you even though annas got confused to :b thanks so much ! :)

Answer 31

you are awesome at geometry @shandelman . Boy God bless you!

Answer 32

I wish I could be I'm amazing with algebra but geometry is my WORST subject :/

Answer 33

sorry tiarapoo it happens to me all the time when i m dealing with geometry :( and i m so sorry for that. i m doing graduation in software engineering so i kinda forgot alot of stuff in geometry :(

Answer 34

lol its fine you still helped me with a lot ! thanks so much for that ! :)

Answer 35

but i lead you to confusion

Answer 36

its okay :b everything worked out in the end that's all that matters :)

Answer 37

ok :)