The area of a rectangular wall of a barn is 45 square feet. its length is 12 feet longer than the width. find the length and width of the wall of the barn.

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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