anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathstudent55
  • mathstudent55
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
anonymous
  • anonymous
170=(2w-4)w once you get here do you distribute?
anonymous
  • anonymous
@mathstudent55

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathstudent55
  • mathstudent55
yes, distribute
anonymous
  • anonymous
170=(2w-4)w 170=2w^2-4w 0=2w^2-4w-170 I dont think im doing this right
mathstudent55
  • mathstudent55
It looks good to me.
mathstudent55
  • mathstudent55
Now try to factor the right side.
anonymous
  • anonymous
can you help me with that, im not sure how
mathstudent55
  • mathstudent55
First, divide both sides by 2
mathstudent55
  • mathstudent55
also, switch sides
mathstudent55
  • mathstudent55
2w^2 - 4w - 170 = 0 Divide both sides by 2
anonymous
  • anonymous
okay so 2w^2-4w-170=0 w^2-2w-85=0?
mathstudent55
  • mathstudent55
Right. Now this kind of factoring involves simply finding two numbers that multiply to -85 and add to -2
mathstudent55
  • mathstudent55
-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
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
|dw:1356497065032:dw|
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
In your case we are solving for w instead of x, and we have a = 1, b = -2, and c = -85.
mathstudent55
  • mathstudent55
|dw:1356497319940:dw|
anonymous
  • anonymous
okay so is the answer w = 2SQRT(86)?
anonymous
  • anonymous
longest ans!
mathstudent55
  • mathstudent55
|dw:1356498098987:dw|
anonymous
  • anonymous
i know, Im so sorry for mathstudent55
mathstudent55
  • mathstudent55
Don't be sorry. this is fun for me.
anonymous
  • anonymous
Okay :) thank you so much that was a lot of help
mathstudent55
  • mathstudent55
I wrote x in the drawing but I meant W. Now you know that W = 1 + sqrt(86) or W = 1 - sqrt(86)
anonymous
  • anonymous
okay, thank you sooooo much
mathstudent55
  • mathstudent55
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)
mathstudent55
  • mathstudent55
You're welcome.

Looking for something else?

Not the answer you are looking for? Search for more explanations.