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# 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 :)

### 1 Answer

- Marley KLv 78 years agoFavorite Answer
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! ;)