SOLUTION: Can someone please help me. I've submitted this problem yesterday at 10:00 am and today at 1:00pm and still haven't gotten a response. Suppose you work in an office and your cu

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can someone please help me. I've submitted this problem yesterday at 10:00 am and today at 1:00pm and still haven't gotten a response. Suppose you work in an office and your cu      Log On


   

Question 188704: Can someone please help me. I've submitted this problem yesterday at 10:00 am and today at 1:00pm and still haven't gotten a response.
Suppose you work in an office and your current cubicle is a square. The company is moving and your new cubicle will be 2 feet longer on one side and 3 feet shorter on the other.
a) Determine the dimensions of your new cubicle based on your original square, which is x feet per side.


x + 2 would be the side 2 feet longer.


x - 3 would be the side 3 feet shorter.


b) Write the equation for the area of your new cubicle.


(x + 2)(x - 3) Area = Length * Width


Using the FOIL method to multiply the polynomials


Note the "FOILy face".


c) If your old cubicle was 8 feet by 8 feet, is your new cubicle larger or smaller and by how much?


8 * 8 = 64 ft2 Size of original cubicle.


82 - 8 - 6 Substitute in value of x which is 8 in this case.


64 - 14


50 ft2 Size of new cubicle


64 - 50 = 14 ft2 New cubicle is 14 square feet smaller than old cubicle.


Using the example above, develop a similar problem in which you change the size of a shape. Show the same steps as above. No graphics needed.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) You are correct. The dimensions are x%2B2 by x-3

b)

Area: A=%28x+%2B+2%29%28x+-+3%29=x%5E2-3x%2B2x-6=x%5E2-x-6


So the area is A=x%5E2-x-6

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c)

Original Area: A=x%5E2=8%5E2=64


New Area: A=x%5E2-x-6=%288%29%5E2-%288%29-6=64-8-6=50


Difference in Areas: 64-50=14


New cubicle is smaller by 14 square feet (since A%5Bn%5D%3CA%5Bo%5D). You are correct.


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d)

Let's say that we start with a square again with side lengths of "x". Now one side is lengthened by 5 while the other is shortened by 2.


So the new dimensions would be x%2B5 by x-2


The new area would be A=%28x%2B5%29%28x-2%29=x%5E2-2x%2B5x-15=x%5E2%2B3x-15

Finally, if x=8, then

Old area: A=8%5E2=64


New area: A=%288%29%5E2%2B3%288%29-15=64%2B24-15=73


Difference in areas: 73-64=9


New area is now 9 square feet larger than the old area.