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.

7 months ago

7 months ago
candygirl200:

sure u could help

7 months ago

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

7 months ago

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

7 months ago

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 $350ft = 2l + 2(2l - 12)$

7 months ago

Are you with me so far?

7 months ago
candygirl200:

yes

7 months ago

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

7 months ago

Where do you think we go from here?

7 months ago
candygirl200:

plug in to find w

7 months ago

Exactly. Which equation would we use?

7 months ago
candygirl200:

the original one

7 months ago

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

7 months ago

Do you understand how I got this?

7 months ago
candygirl200:

yes thanks

7 months ago