SOLUTION: you want to fence off a rectangular area of yard using the back side of you house as one of the sides. you have a total of 150 yards of fence. if the area of the fenced in portion

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Question 1145245: you want to fence off a rectangular area of yard using the back side of you house as one of the sides. you have a total of 150 yards of fence. if the area of the fenced in portion comes to 2,812 square yards, what are the dimensions of the fenced-in area?
Found 3 solutions by ikleyn, greenestamps, josmiceli:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
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UNCLEAR.

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

The 150 yards of fence is the width twice and the length once, because the side of the house is one side of the fenced area:

The area (length times width) is 2812:

There are always many possible paths to a solution; given those two equations probably the easiest is to solve the first equation for l and substitute in the second equation.

That quadratic does in fact factor. But most students are not going to see how, so they will probably use the quadratic formula, or maybe a graphing calculator.

I leave it to you to do the work to finish the problem.

It should be noted that the quadratic equation shown has two positive roots, leading to two different possibilities for the dimensions of the fenced-in area.

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By the way....

That is a VERY LONG side of a house!!!

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let = the sides perpendicular to the house
The 3rd side is:

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and

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When ,

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When

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The fenced in area can be either:
37 x 76 or
38 x 74
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check:

and

OK