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.

10 months ago
Shadow:

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

10 months ago
candygirl200:

sure u could help

10 months ago
Shadow:

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

10 months 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

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

10 months ago
Shadow:

Are you with me so far?

10 months ago
candygirl200:

yes

10 months ago
Shadow:

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

10 months ago
Shadow:

Where do you think we go from here?

10 months ago
candygirl200:

plug in to find w

10 months ago
Shadow:

Exactly. Which equation would we use?

10 months ago
candygirl200:

the original one

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

10 months ago
Shadow:

Do you understand how I got this?

10 months ago
candygirl200:

yes thanks

10 months ago
Shadow:

No problem :)

10 months ago