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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (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, 40%2A32 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 %2840-2x%29%2832-2x%29.

Think about the two separate parts and the total.
Border area plus slab area is the piece of land area.
B for Border Area,
B%2B%2840-2x%29%2832-2x%29=40%2A32
B=40%2A32-%2840-2x%29%2832-2x%29

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: %2840-2x%29%2832-2x%29

(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.