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?

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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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|dw:1441124255042:dw|
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|
whoa....

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can u make this a bit easier ?
furthermore, we have: \[\Large AB = {L_2} + {L_1} = 3{L_1} + {L_1} = 4{L_1}\]
finally, from your data, we have: \[\Large 5 = AB = 4{L_1}\]
.....
please solve this equation for L1: \[\Large 5 = 4{L_1}\]
with A2 and A1 I meant the area of the largest shaded square and the area of the smallest shaded square respectively
wow..... i really dont understand your explanation.
|dw:1441125356826:dw|
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
please refer to my drawings above
now, we can write this: \[\Large {A_2} = L_2^2\] and: \[\Large {A_1} = L_1^2\]
nevermind u make things too complicated
HI!!
save me Misty
lol this looks confusing but it can't be too bad can it?
yea it's confusing... I've made no progress..
the area of the big square is 25 right?
yea so the length of one side is 5
ok so the only thing i don't get is what "long shaded square" means is that the big square ?
the bigger square inside the square yes
i thought it would be |dw:1441127490171:dw|
so |dw:1441127538111:dw|
hold on is that the equation you derived?
No i got that from the problem it says the longer shaded is 9 times the area of the smaller shaded
cause it aint what i get
what u get?
|dw:1441127697875:dw|
we know two things one is that \(x+y=5\) because the length is 5 the other is that \(x^2=9y^2\)
so far so good?
y is it 9y instead of 9x? i thought they said the longer shaded is 9 times the area of the smaller shaded?
oh yeah you are right\[9x^2=y^2\]
since \(x+y=5\) we know \(y=5-x\)
so the equation to solve is \[9x^2=(5-x)^2\]
ohhhhhhhhhhhhhhhhhhhhhhhh you just made me understand with the 9x^2 = y^2
ok good! multiply out, put on one side of the equal sign, get \[8 x^2+10 x-25 = 0\]
|dw:1441127982300:dw|
ok that works too
\[3x=y\\ x+y=5\]
|dw:1441128046691:dw|