Question

Ben fenced his backyard using 350 feet of fencing. The width of his yard is 12 feet less than twice the length. Write an equation that can be used to determine the dimensions of his yard and solve.

Answer 1

Hello @candygirl200 Do you mind if I help you today?

Answer 2

sure u could help

Answer 3

"The width of his yard is 12 feet less than twice the length."

w = 2l - 12

Where,
w = width
l = length

Answer 4

Going to assume that this is a rectangular backyard (as they usually are).

The formula for the perimeter of a rectangle can be written as,
P = 2l + 2w

Where P is the perimeter

Answer 5

Right now we have three variables. P, w, and l

In order to solve for a variable in any algebraic equation, we must have only ONE unknown.

"Ben fenced his backyard using 350 feet of fencing."

With this sentence we know that P = 350ft as a fence goes around the "perimeter"

Then with that information we start working some magic with our two equations that I showed.

w = 2l - 12

P = 2l + 2w

We will be using the second one as it expresses the dimensions of the yard in terms of the perimeter.

We can replace P with 350ft

350ft = 2l + 2w

We have w defined in our earlier equation, so we can do

\[350ft = 2l + 2(2l - 12) \]

Answer 6

Are you with me so far?

Answer 7

yes

Answer 8

\[350 = 2l + 2(2l - 12) \]

We solve for our unknown, the length

\[350 = 2l + 4l - 24\]

\[350 = 6l - 24\]

\[374 = 6l\]

\[l = \frac{ 187 }{ 3 }\]

Answer 9

Where do you think we go from here?

Answer 10

plug in to find w

Answer 11

Exactly. Which equation would we use?

Answer 12

the original one

Answer 13

We can use both P = 2l + 2w and w = 2l - 12, but it is easier to use the second one since it is already in terms of w.

\[w = 2l - 12\]

\[w = 2(\frac{ 187 }{ 3 }) - 12\]

\[w = \frac{ 374 }{ 3 } - 12\]

\[w = \frac{ 374 }{ 3 } - \frac{ 36 }{ 3 }\]

\[w = \frac{ 338 }{ 3 }\]

Answer 14

Do you understand how I got this?

Answer 15

yes
thanks

Answer 16

No problem :)