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?

Question

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?

mathstudent55 · Answer

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 · Answer

170=(2w-4)w once you get here do you distribute?

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

yes, distribute

anonymous · Answer

170=(2w-4)w
170=2w^2-4w
0=2w^2-4w-170
I dont think im doing this right

mathstudent55 · Answer

It looks good to me.

mathstudent55 · Answer

Now try to factor the right side.

anonymous · Answer

can you help me with that, im not sure how

mathstudent55 · Answer

First, divide both sides by 2

mathstudent55 · Answer

also, switch sides

mathstudent55 · Answer

2w^2 - 4w - 170 = 0
Divide both sides by 2

anonymous · Answer

okay so 2w^2-4w-170=0
            w^2-2w-85=0?

mathstudent55 · Answer

Right. Now this kind of factoring involves simply finding two numbers that multiply to
-85 and add to -2

mathstudent55 · Answer

-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 · Answer

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 · Answer

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