SOLUTION: The topic of my question is Quadratic Area Problems but that was not a choice, so I just went with parabolas. Also, this specific question has about 7 parts and I do not know how t

Question 1002154: The topic of my question is Quadratic Area Problems but that was not a choice, so I just went with parabolas. Also, this specific question has about 7 parts and I do not know how to even begin on any of them.
A homeowner has a rectangular piece of land 40 feet by 32 feet. He wants to place a rectangle shaped slab for a house on the land in such a way there is a uniform piece of lawn around it. Let "X" equal the width of the strip of surrounding lawn.
a) write an equation that expresses the area of slab in terms of "x"
b) what is the y-intercept value
c) if the lawn has a width of 16ft, what is the area of the slab?
d) what is the area of the slab if x is 12 feet
e) what is the width of the lawn if the area must be 900 square feet
f) what is the width of the lawn if the area is at most 900 square feet
g) what is the width of the lawn if the area is at least 600 square feet
Please help. Thank you so much!

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
This works better if we can draw a picture or figure - not easy enough to do here.

Total piece of land area, square feet.

The rectangular slab, you only know that its placement in the middle of the piece of land must make a uniform width distance x between the boundary of the piece of land and a side of the slab.

The area which the slab covers is .

Think about the two separate parts and the total.
Border area plus slab area is the piece of land area.
B for Border Area,

A brief re-read reminds us that "lawn" is for "border". There is the lawn and the slab.

That is for beginning and analyzing.

(b) You want to find the y-intercepts? What is (40-2x)(32-2x) when x is 0? That will give the y-axis intercept.

(a) There done earlier:

(c) If x=16 then what is the area of the slab? Substitute into the expression derived already.

For the rest, you should be able to think your way through.
RELATED QUESTIONS
I was not sure which topic to place my question under, so I just picked one. I hope that (answered by Fombitz)

Hi, So I missed my Pre-Ap Algebra II class, and I was wondering how I would be able to... (answered by josgarithmetic,MathTherapy)

This question is not directly related a particular topic in Math. I am looking for advice (answered by rothauserc,MathLover1)

In the problem... The Tadashi corporation manufactures a large speaker and a small... (answered by acerX)

you do not have the topic that is appropriate for my question. Ill just type it anyway... (answered by Earlsdon)

I just finished a math exam and theres one question that I just couldn't figure out. It... (answered by richard1234)

Hey there! I have a few question, and it said not to dump everything on here. Sadly my... (answered by richwmiller)

Here is my problem: Sarah went to Jen house at 10:00 with 40 mph.The distance from her... (answered by josmiceli)

i'm not quite sure if this is evaluation of expressions, parentheses, i'm just confused!... (answered by Fombitz)