Square lot. Sam has a lot that he thought was a square, 200 feet by 200 feet. When he had it surveyed, he discovered that one side was x feet longer than he thought and that the other side was x feet shorter than he thought.

a).
Find a polynomial A(x) that represents the new area.
b).
Find A(2)
c).
If x=2 feet then how much less area does he have than he thought he had?
Answer:
a).
A(x)=(200-x)*(200+x)
A(x)=40,000-x^2
b).
A(2)=40,000-(2)^2
A(2)=40,000-4
A(2)=39,996 feet^2
c).
Initial area= 200*200=40,000 feet^2
Present area A(2)=39,996 feet^2
40,000 – 39,996= 4 feet ^2
I need to know if i done this correctly.

All of your answers are correct, and

you did a good job of showing your
work. Good job!!

Thank you so much!

Your answers are correct. Well done!

To find the new area of the lot, you correctly set up the polynomial A(x) as (200-x)*(200+x). This represents the length of one side of the lot being x feet longer and the other side being x feet shorter. Simplifying this expression gives you A(x) = 40,000 - x^2.

When evaluating A(2), you substituted x = 2 into the polynomial: A(2) = 40,000 - (2)^2 = 40,000 - 4 = 39,996 feet^2.

Lastly, to find the difference in area between what Sam initially thought and the actual area with x = 2 feet, you subtracted the initial area (40,000 feet^2) from the present area (A(2) = 39,996 feet^2), which correctly gives you 4 feet^2.

Overall, your calculations and explanations are correct. Great job!