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fortytwo
 3 years ago
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?
fortytwo
 3 years ago
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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mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2The 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

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0170=(2w4)w once you get here do you distribute?

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0170=(2w4)w 170=2w^24w 0=2w^24w170 I dont think im doing this right

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2It looks good to me.

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2Now try to factor the right side.

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0can you help me with that, im not sure how

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2First, divide both sides by 2

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2also, switch sides

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.22w^2  4w  170 = 0 Divide both sides by 2

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0okay so 2w^24w170=0 w^22w85=0?

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2Right. Now this kind of factoring involves simply finding two numbers that multiply to 85 and add to 2

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.285 = 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

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2As 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.

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1356497065032:dw

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2That 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.

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

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1356497319940:dw

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0okay so is the answer w = 2SQRT(86)?

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1356498098987:dw

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0i know, Im so sorry for mathstudent55

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2Don't be sorry. this is fun for me.

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0Okay :) thank you so much that was a lot of help

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2I wrote x in the drawing but I meant W. Now you know that W = 1 + sqrt(86) or W = 1  sqrt(86)

fortytwo
 3 years ago
Best ResponseYou've already chosen the best response.0okay, thank you sooooo much

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.2First 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)
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