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|dw:1441124255042:dw|

whoa....

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:
\[\Large 5 = 4{L_1}\]

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

|dw:1441125356826:dw|

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?

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|