you are planning to make a dog pen for your dog, algebra. you have purchased 100 ft of fencing. you need the legnth of the pen to be 10 ft more than the width. Write and equation and solve for W.

Question

Please help! I am stuck on this problem!!

Answer 1

You have two variables, width and length, so you need two equations. From the question you know that the dog pen has to be rectangular with four sides: two widths (W) and two lengths (L), which together add up to 100 feet. So the first equation you can write is

2L + 2W = 100 feet

in English, "Two lengths plus two widths equal 100 feet."

The second thing you know is that the length is 10 feet longer than the width, so the second equation you can write is

L = W + 10

Now that you have defined L in terms of W you can solve the problem.

First substitute "W + 10" for L in the first equation

2(W + 10) + 2W = 100

Get rid of the parentheses by multiplying by 2

2W + 20 + 2W = 100

Add like terms

4W + 20 = 100

Subtract 20 from both sides

4W = 80

Divide both sides by 4,

W = 20

then check your answer:

If W = 20 then L = 30 (L = W + 10),

and 2L + 2W should = 100

2(30) + 2(20) = 100

which it does.

Answer 2

If you have 100 ft of fencing, that is the perimeter.

Let w = the width of the dog pen

w+10 = the length of the dog pen (based on the conditions given)

Perimeter = width + width + length + length

100 = w+w+w+10+w+10

100=4w+20 subtract 20 from both sides

80=4w Divide both sides by 4

20 ft=w

Answer 3

here You bought 100ft of fencing,

if we say Length is L and Width is W

From the formula of perimeter we can write, 2*(L + W ) = 100

length of dog pen 10 ft more than the width , we can write L = 10+ W ,

substituting this value of L in the above equation we get,

2* ( 10+ W + W ) = 100

dividing both sides by 2,

10+ W + W = 100/2= 50

10+ 2W = 50

subtracting 10 on both sides,

2W = 50-10= 40

dividing both sides by 2

W = 40 / 2 = 20

so Width is 20 ft Ans

and L = W + 10 = 20+ 10 = 30 ft