Question

Rectangle A has an area of 16 - x2. Rectangle B has an area of x2 + 2x - 24. In simplest form, what is the ratio of the area of Rectangle A to the area of Rectangle B? Show your work.

Answer 1

@wolf1728

Answer 2

Here I am

Answer 3

Loll welcome

Answer 4

16 - x2 = (4 +x) • (4 -x)
x2 + 2x - 24 = (x +6) • (x -4)
That's a start

Answer 5

okay

Answer 6

dont we have to cross out the 4

Answer 7

no forget it

Answer 8

Should I divide 1 by the other?
(x +6) • (x -4) / (4 +x) • (4 -x)

Answer 9

yes

Answer 10

= (-x - 4)/(x + 6

Answer 11

Seems that nothing cancels out in that division does it?

Answer 12

no

Answer 13

Maybe there's another way

Answer 14

sorry serious lag

Answer 15

If we get the roots of the equations x= -6 and x = 4
Does that help?

Answer 16

i'm gonna be honest im am not sure

Answer 17

maybe there's more I can do

Answer 18

maybe..

Answer 19

well you have done a lot its just me i'm beat

Answer 20

Well, I was thinking what might be the factors of an area of 16-x²
The root of that equation is 4 and so Area = 16 -4² = 0
The other root -4 makes the Area = 16 -(-4²) = 0
Something seems strange about that 16 -x² equation

Answer 21

what seems strange?

Answer 22

How about
x² + 2x - 24 = 16 - x²

That can't be correct because the 2 areas are different.
*******************************************************
What seems strange about 16 -x² is that the roots of it make the Area = 0

Answer 23

Had a feeling okay so how do we make this right?

Answer 24

I don't know. How about the area of the rectangle that is
x² + 2x - 24
The one positive root of that is 4 so let's say
Area = 4² +2 • 4 + 24
Area = 16 + 8 + 24
Area = 48
That seems correct

Answer 25

Hmm it does seem correct

Answer 26

Nope - there's a mistake
Area = 4² +2 • 4 + 24 is wrong
SHOULD BE -24

Answer 27

That makes the other area = 0 also.
This is a weird problem

Answer 28

:S oh

Answer 29

let me show you something maybe you'll find it a little more understanding than me

Answer 30

Are we supposed to be comparing the area of non-existant rectangles?

Answer 31

i do not think so

Answer 32

http://openstudy.com/study#/updates/503aa45ae4b0edee4f0da8e1

Answer 33

take a look at it please

Answer 34

Sure will

Answer 35

ok thanks

Answer 36

I looked. 16 -x² was factored incorrectly. It equals (4 +x)(4 -x)
They had an x-4 in their answer which is wrong.

Answer 37

I'm glad you saw that because i dont know how to make sense of this

Answer 38

I was hoping they had an answer.

Answer 39

me too okay so this is something someone said

Answer 40

A/B

(16 - x^2) / (x^2 + 2x - 24)
(4 - x)(4 + x) / ( (x + 6)(x - 4) )
-(x - 4)(4 + x) / ( (x + 6)(x - 4) )
-(4 + x) / ( (x + 6) ) <===== the ratio

Answer 41

I calculated
(x +6) • (x -4) / (4 +x) • (4 -x)
I think they messed around with the (4-x) term. (again)
How about the ratio of the areas is
(x +6) • (x -4) / (4 +x) • (4 -x) ?

Answer 42

?

Answer 43

or the way they posted their ratio
(4 +x) • (4 -x) / (x +6) • (x -4)

Answer 44

ohh

Answer 45

A/B
= (16 - x^2)/(x^2 + 2x -24)
= ((4 - x)(4 + x))/((x + 6)(x - 4))
= (-x - 4)/(x + 6)

Answer 46

what about that

Answer 47

You change (4-x) on the second line to
(-x-4) on the third line
and what cancels out with the x-4 in the denominator?

Answer 48

I didnt do it

Answer 49

:( i was just showing you something i saw

Answer 50

Sorry well somebody did it and they did it wrong.
Hmmmm and no closer to the solution.
Is this problem for an online test or school?

Answer 51

online test flvs to be exact

Answer 52

Is there anyway you could ask a question about this problem?

Answer 53

i wish i could get out the test and continue tmr but i cant it is one access only then your locked out

Answer 54

My teacher is asleep i think nd she wont be back till 8 or later by that time ill be timed out the test

Answer 55

Well then I don't know what to say.
Maybe the answer is (x +6) • (x -4) / (4 +x) • (4 -x)

Answer 56

Okay i will take it and run with it but can you show me what to right in my answer

Answer 57

then i have the last question i'll put it in a different thread afterwards

Answer 58

What I would say is
the ratio of Area B to Area A is (x+6)•(x-4) / (4+x)•(4-x)
This cannot be reduced any further.

Answer 59

k thank you

Answer 60

hope it helps

Answer 61

it did

Answer 62

Well thanks

Answer 63

Yvw

Answer 64

Well maybe it's time to leave OpenStudy

Answer 65

No please dont go just yet i have one more question im dying to get this test done

Answer 66

Okay - glad I just didn't leave

Answer 67

Phew* new thread okay

Answer 68

Sure

Answer 69

i'll tag you