how to find the maximum value for this problem?
a police officer has 400m of yellow tape to seal off the area of a crime scene. what is the maximum area that can be enclosed?

i already know that the answer is 10,000 but i just need someone to explain the steps to getting the answer. thanks in advance :)
you don't say that the area must be a rectangle. the true largest area would be a circle, with the circumference equal to 400m and the area would be 12,732.4 m^2. however, evidently, the area is restricted to a rectangle, in which case the maximum area is a square, and the side of the square will be 
400/4 = 100 m. the area is 100x100 = 10,000 m^2.
algebraically,
let x = one pair of opposite sides
(400-2x)/2 = 200-x = the other pair of opposite sides

area = a(x) = x(200 - x) = -x^2 + 200x
x-coordinate of vertex = -b/2a = 200/2 = 100
a(100) = 10,000

that's it! ;)
d = 21 m
r =![](https://img-nm%20mnimgs%20com/img/study_content/curr/1/7/3/41/1541/chapter%2011_html_96a2a55%20gif)
circumference = 2πr =![](https://img-nm%20mnimgs%20com/img/study_content/curr/1/7/3/41/1541/chapter%2011_html_521eed1b%20gif)= 66 m
length of rope required for fencing = 2 × 66 m = 132 m
cost of 1 m rope = rs 4
cost of 132 m rope = 4 × 132 = rs 528 Correct option is A) 9.378 m2


![](https://lh3.googleusercontent.com/-UueuqyijXPQ/YLtK0v0m9CI/AAAAAAAABro/xFcfQOQAOx8jHAtpqiORvW_8DRFX1yK3ACLcBGAsYHQ/image.png)


result must have significant figures equal to least figures being multiplid do area of metal sheet 9.378 m2  (four significant digits) You need to hire a lawyer immediately. The police could be interrogating him and he can be confessing to serious crimes ![](https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4110270/2012_11_30_15_28_05/vvnzofse6383734697724592802%20png)


let the length of path be a m


total area ![](https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4110270/2012_11_30_15_28_05/ceaxujzx7923478049123545928%20png)


area of lawn = total area â€“ area of
path

![](https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/1800204/2012_12_04_21_09_56/mathmlequation2002748073868866733%20png)


area of lawn


![](https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/4110270/2012_11_30_15_28_05/dwqusyms3311632565229211681%20png) the given equations arex2 + y2 = 16 …(i)and y2 = 6x …(ii)on solving the equation (i) and (ii),or x2 + 6x = 16or x2 + 6x – 16 = 0or (x + 8)(x – 2) = 0or x = 2 or – 8 is not possible solution∴ when x = 2, y = ± = ± = ±equation (i) is a circle with centre (0, 0) and meets axes at (±4,0), (0,±4)equation (ii) represents a parabola with axis as x - axis.points of intersection are a () and c (2,)these are shown in the graph below:area bounded by the circle and parabola= 2[area (oado) + area (adba)]area of circle = π(r) 2= π(4)2= 16π sq. unitsthus, required areathe area of the circle x2 + y2 = 16 which is exterior the parabola y2 = 6x is given the boundaries of the area to be found are,• the curve • the x-axis• x = 0 (y-axis)• x = 4 (a line parallel toy-axis)as per the given boundaries,• the curve,is a curve with vertex at .• x=2 is parallel toy-axis at 2 units away from the y-axis.• x=0 is the y-axis.• the four boundaries of the region to be found are,•point a, where the curve y2 = 6x + 4 and x=0 meet.•point b, where the curve y2 = 6x + 4 and x=2 meet.•point c, where the x-axis and x=2 meet i.e. c(2,0).•point o, or the origin i.e. o(0,0).area of the required region = area of oabc.[using the formula ]the area of the required region area of trapezium = area of trapezium = = therefore = 24 cm Hopefully, you called the police right when this occurred and have a police report. It will be up to the solicitor's office on whether or not to file charges. Unfortunately, this person may be judgment proof. This means that even if you were to sue them and successfully obtain a judgment, you may have no way of actually collecting against that judgment. total cost of fencing = rs 9600
rate of fencing = rs 24
then, perimeter of field = cost/rate = 9600/24 = 400mts
let the length and breadth of the rectangular field be 5x and
3x
then perimeter= 2(l+b)
= 2(5x+3x)
= 2*8x = 16x
but the perimeter of the given field is 400 m
so, 16x = 400
x = 400/16 = 25
length of the field = 5*25mts = 125mts
breadth of the field = 3*25mts = 75mts Unlawful carrying of a pistol carries a sentence of up to a year and a fine of $1000.


Even though finances are an issue for you, I would highly recommend retaining an attorney to assist you with your defense.


Best of luck.