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?

- anonymous

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- anonymous

|dw:1441124255042:dw|

- 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

whoa....

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## More answers

- anonymous

can u make this a bit easier ?

- Michele_Laino

furthermore, we have:
\[\Large AB = {L_2} + {L_1} = 3{L_1} + {L_1} = 4{L_1}\]

- Michele_Laino

finally, from your data, we have:
\[\Large 5 = AB = 4{L_1}\]

- anonymous

.....

- Michele_Laino

please solve this equation for L1:
\[\Large 5 = 4{L_1}\]

- 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

wow..... i really dont understand your explanation.

- anonymous

|dw:1441125356826:dw|

- 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

please refer to my drawings above

- Michele_Laino

now, we can write this:
\[\Large {A_2} = L_2^2\]
and:
\[\Large {A_1} = L_1^2\]

- anonymous

nevermind u make things too complicated

- anonymous

@Nnesha

- misty1212

HI!!

- anonymous

save me Misty

- misty1212

lol this looks confusing but it can't be too bad can it?

- anonymous

yea it's confusing... I've made no progress..

- misty1212

the area of the big square is 25 right?

- anonymous

yea so the length of one side is 5

- misty1212

ok so the only thing i don't get is what "long shaded square" means
is that the big square ?

- anonymous

the bigger square inside the square yes

- anonymous

i thought it would be |dw:1441127490171:dw|

- anonymous

so |dw:1441127538111:dw|

- misty1212

hold on is that the equation you derived?

- anonymous

No i got that from the problem it says the longer shaded is 9 times the area of the smaller shaded

- misty1212

cause it aint what i get

- anonymous

what u get?

- misty1212

|dw:1441127697875:dw|

- 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

so far so good?

- 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

oh yeah you are right\[9x^2=y^2\]

- misty1212

since \(x+y=5\) we know \(y=5-x\)

- misty1212

so the equation to solve is
\[9x^2=(5-x)^2\]

- anonymous

ohhhhhhhhhhhhhhhhhhhhhhhh you just made me understand with the 9x^2 = y^2

- misty1212

ok good!
multiply out, put on one side of the equal sign, get \[8 x^2+10 x-25 = 0\]

- anonymous

|dw:1441127982300:dw|

- misty1212

ok that works too

- misty1212

\[3x=y\\
x+y=5\]

- anonymous

|dw:1441128046691:dw|