anonymous
  • anonymous
Help please.... =*( If square ABCD has area 25, and the shape of the longer shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1441124255042:dw|
Michele_Laino
  • Michele_Laino
we can write this: \[\Large {A_2} = 9{A_1} \Rightarrow L_2^2 = 9L_1^2 \Rightarrow {L_2} = 3{L_1}\] |dw:1441124497875:dw|
anonymous
  • anonymous
whoa....

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anonymous
  • anonymous
can u make this a bit easier ?
Michele_Laino
  • Michele_Laino
furthermore, we have: \[\Large AB = {L_2} + {L_1} = 3{L_1} + {L_1} = 4{L_1}\]
Michele_Laino
  • Michele_Laino
finally, from your data, we have: \[\Large 5 = AB = 4{L_1}\]
anonymous
  • anonymous
.....
Michele_Laino
  • Michele_Laino
please solve this equation for L1: \[\Large 5 = 4{L_1}\]
Michele_Laino
  • Michele_Laino
with A2 and A1 I meant the area of the largest shaded square and the area of the smallest shaded square respectively
anonymous
  • anonymous
wow..... i really dont understand your explanation.
anonymous
  • anonymous
|dw:1441125356826:dw|
Michele_Laino
  • Michele_Laino
from the text of your problem I read: "the shape of the longer shaded square is 9 times the area of the smaller shaded square" that statement is modeled by this equation: \[\Large {A_2} = 9{A_1}\] where with A2 and A1 are the area of the largest shaded square and the area of the smallest shaded square respectively
Michele_Laino
  • Michele_Laino
please refer to my drawings above
Michele_Laino
  • Michele_Laino
now, we can write this: \[\Large {A_2} = L_2^2\] and: \[\Large {A_1} = L_1^2\]
anonymous
  • anonymous
nevermind u make things too complicated
anonymous
  • anonymous
@Nnesha
misty1212
  • misty1212
HI!!
anonymous
  • anonymous
save me Misty
misty1212
  • misty1212
lol this looks confusing but it can't be too bad can it?
anonymous
  • anonymous
yea it's confusing... I've made no progress..
misty1212
  • misty1212
the area of the big square is 25 right?
anonymous
  • anonymous
yea so the length of one side is 5
misty1212
  • misty1212
ok so the only thing i don't get is what "long shaded square" means is that the big square ?
anonymous
  • anonymous
the bigger square inside the square yes
anonymous
  • anonymous
i thought it would be |dw:1441127490171:dw|
anonymous
  • anonymous
so |dw:1441127538111:dw|
misty1212
  • misty1212
hold on is that the equation you derived?
anonymous
  • anonymous
No i got that from the problem it says the longer shaded is 9 times the area of the smaller shaded
misty1212
  • misty1212
cause it aint what i get
anonymous
  • anonymous
what u get?
misty1212
  • misty1212
|dw:1441127697875:dw|
misty1212
  • misty1212
we know two things one is that \(x+y=5\) because the length is 5 the other is that \(x^2=9y^2\)
misty1212
  • misty1212
so far so good?
anonymous
  • anonymous
y is it 9y instead of 9x? i thought they said the longer shaded is 9 times the area of the smaller shaded?
misty1212
  • misty1212
oh yeah you are right\[9x^2=y^2\]
misty1212
  • misty1212
since \(x+y=5\) we know \(y=5-x\)
misty1212
  • misty1212
so the equation to solve is \[9x^2=(5-x)^2\]
anonymous
  • anonymous
ohhhhhhhhhhhhhhhhhhhhhhhh you just made me understand with the 9x^2 = y^2
misty1212
  • misty1212
ok good! multiply out, put on one side of the equal sign, get \[8 x^2+10 x-25 = 0\]
anonymous
  • anonymous
|dw:1441127982300:dw|
misty1212
  • misty1212
ok that works too
misty1212
  • misty1212
\[3x=y\\ x+y=5\]
anonymous
  • anonymous
|dw:1441128046691:dw|
misty1212
  • misty1212
so really it is just a linear equation to solve namely \[x+3x=5\]
anonymous
  • anonymous
THANKS MISTYYYYYYYYYYYYYYY!!! <333333 love you guuuurl
misty1212
  • misty1212
yeah your method is much better than my stupid quadratic!
misty1212
  • misty1212
lol luv u 2, even though you are not my mama boyfriend (i hope)\[\color\magenta\heartsuit\]
anonymous
  • anonymous
lolol ^_^
Michele_Laino
  • Michele_Laino
Please note that my procedure is not confusing, it is a step by step procedure in order to get the solution, what has been called with x and y, I called with L1 and L2 respectively, furthermore the result from my last equation is: \[\Large {L_1} = \frac{5}{4}\] namely the same answer, using different symbols @misty1212 @yomamabf

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