Answer:
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Step-by-step explanation:
by using the formula for area: A= L x W substitute in what you know: A = 54 , the length in terms of the width so use
L=12 + 2W.
Now when everything is plugged in you now have: 54 = (12 + 2W) x W
Then use the Distributive Property to simplify: 54 = 12W + 2W2
Since you know have a quadratic to solve get it in the form ax2+bx + c = 0 so that you can solve it:
You do this by subtracting 54 from both sides and putting the 2W2 first so now it looks like this:
2W2 + 12W -54 = 0
Using the quadratic formula where a =2, b = 12, and c = -54.
Find b2-4ac which is the discriminant:
(12)2-4*2*(-54)=576
Take the square root of 576= 24
Now substitute the rest of the values into the Quadratic Formula:
It will look something like this: W = (-b plus or minus the square root of the discriminant)/2a
The two possible answers are:
W = (-12 + 24)/4 and W = (-12 - 24)/4
W = 12/4= 3 and W = -36/4= -9 (This second answer isn't possible because length can't be negative)
So the answer is:
Width = 3 feet Length = 12 + 2W = 12 + 2*3= 12 + 6 = 18 feet
This checks because A = L x W and 54 = 18 x 3
