candygirl200:

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.

1 year ago
Shadow:

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

1 year ago
candygirl200:

sure u could help

1 year ago
Shadow:

"The width of his yard is 12 feet less than twice the length." w = 2l - 12 Where, w = width l = length

1 year ago
Shadow:

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

1 year ago
Shadow:

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

1 year ago
Shadow:

Are you with me so far?

1 year ago
candygirl200:

yes

1 year ago
Shadow:

\[350 = 2l + 2(2l - 12) \] We solve for our unknown, the length \[350 = 2l + 4l - 24\] \[350 = 6l - 24\] \[374 = 6l\] \[l = \frac{ 187 }{ 3 }\]

1 year ago
Shadow:

Where do you think we go from here?

1 year ago
candygirl200:

plug in to find w

1 year ago
Shadow:

Exactly. Which equation would we use?

1 year ago
candygirl200:

the original one

1 year ago
Shadow:

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. \[w = 2l - 12\] \[w = 2(\frac{ 187 }{ 3 }) - 12\] \[w = \frac{ 374 }{ 3 } - 12\] \[w = \frac{ 374 }{ 3 } - \frac{ 36 }{ 3 }\] \[w = \frac{ 338 }{ 3 }\]

1 year ago
Shadow:

Do you understand how I got this?

1 year ago
candygirl200:

yes thanks

1 year ago
Shadow:

No problem :)

1 year ago