Graphing calculator aint' gon' help here. You're going to have to solve a quadratic equation, but you won't have the C coefficient to plug into the TI.
Let's get started.
Here's what we know:
A = L x W
L = W + 6
Let's substitute to get that pesky L out of there:
A = (W + 6) x W
A = (W^2) + 6W
Well, shit. If it weren't for that squared term, we could've just solved here. Instead, it's time for... the QUADRATIC EQUATION WEEEEEEE!!!1!!!!1
(W^2) + 6W - A = 0
W = -6 + sqrt(36 + 4A)/2
Thankfully, we can simplify the radical. 4 is a factor we can pull out. Shall we?
W = -6 + 2sqrt(9 + A)/2
Another step of simplification. 2 is a common factor.
W = -3 + sqrt(9 + A)
And we have our answer.
B) sqrt(9 + A) - 3
Oops, forgot something. The quadratic formula has a +/- but I just put + so what gives? Well, for one, there are no negative answers in the choices. And, because of the context, that makes sense: you can't have a negative side length.
English
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Thanks! Now I know another way to solve this. WHat I did what was called complete the Square...
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You're a braver man than I. Completing the square sucks hard.