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Margaret is planning a rectangular garden. Its length is 4 feet less than twice its width. Its area is 170ft^2. what are the dimensions of the garden?

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The area of a rectangle is A = LW, where A = area, L = length, W = width The width is W The length is 4 feet less than twice the width twice the width = 2W four feet less than twice the width = 2W - 4 L = 2W - 4 A = LW, but A = 170, so 170 = LW L = 2W - 4 Since the second equation is already solved for L, just plug that into the first equation and solve for W. Then plug in W in the second equation and solve for L
170=(2w-4)w once you get here do you distribute?

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yes, distribute
170=(2w-4)w 170=2w^2-4w 0=2w^2-4w-170 I dont think im doing this right
It looks good to me.
Now try to factor the right side.
can you help me with that, im not sure how
First, divide both sides by 2
also, switch sides
2w^2 - 4w - 170 = 0 Divide both sides by 2
okay so 2w^2-4w-170=0 w^2-2w-85=0?
Right. Now this kind of factoring involves simply finding two numbers that multiply to -85 and add to -2
-85 = -85 x 1 -85 + 1 = -84 -85 = 85 x -1 85 - 1 = 84 -85 = -17 x 5 -17 + 5 = -12 -85 = 17 x (-5) 17 - 5 = 12
As you can see, there are no two such numbers. This cannot be factored. We now use the quadratic equation. Let's move to a drawing.
That is the quadratic formula. If you have an equation of the form ax^2 + bx + c = 0, you enter the coefficients a, b, and c into the quadratic formula, as shown above, and you get the solution to the equation.
In your case we are solving for w instead of x, and we have a = 1, b = -2, and c = -85.
okay so is the answer w = 2SQRT(86)?
longest ans!
i know, Im so sorry for mathstudent55
Don't be sorry. this is fun for me.
Okay :) thank you so much that was a lot of help
I wrote x in the drawing but I meant W. Now you know that W = 1 + sqrt(86) or W = 1 - sqrt(86)
okay, thank you sooooo much
First look at 1 - sqrt(86). It's a negative number. A width can't be negative, so discard that solution. W = 1 + sqrt(86) L = 2W - 4 = 2(1 + sqrt(86)) - 4 = 2 + 2sqrt(86) - 4 = 2sqrt(86) - 2 So final answer is: L = 2sqrt(86) - 2 W = 1 + sqrt(86)
You're welcome.

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