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fortytwo
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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?
 one year ago
 one year ago
fortytwo Group Title
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?
 one year ago
 one year ago

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mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
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
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
170=(2w4)w once you get here do you distribute?
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
@mathstudent55
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
yes, distribute
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
170=(2w4)w 170=2w^24w 0=2w^24w170 I dont think im doing this right
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
It looks good to me.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
Now try to factor the right side.
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
can you help me with that, im not sure how
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
First, divide both sides by 2
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
also, switch sides
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
2w^2  4w  170 = 0 Divide both sides by 2
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
okay so 2w^24w170=0 w^22w85=0?
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
Right. Now this kind of factoring involves simply finding two numbers that multiply to 85 and add to 2
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
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
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
dw:1356497065032:dw
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
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.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
In your case we are solving for w instead of x, and we have a = 1, b = 2, and c = 85.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
dw:1356497319940:dw
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
okay so is the answer w = 2SQRT(86)?
 one year ago

Raja99 Group TitleBest ResponseYou've already chosen the best response.0
longest ans!
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
dw:1356498098987:dw
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
i know, Im so sorry for mathstudent55
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
Don't be sorry. this is fun for me.
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
Okay :) thank you so much that was a lot of help
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
I wrote x in the drawing but I meant W. Now you know that W = 1 + sqrt(86) or W = 1  sqrt(86)
 one year ago

fortytwo Group TitleBest ResponseYou've already chosen the best response.0
okay, thank you sooooo much
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
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)
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.1
You're welcome.
 one year ago
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