Question

Among all rectangles having a perimeter of 25m, find the dimensions of the one with the largest area​

Answer 1

It's a square 6.25 * 6.25 m.

Explanation:

We can do this using calculus.

Let the length of the rectangle be x m.

2x + 2w = 25 where w = the width.

2w = 25 - 2x

w = 12.5 - x

So the area A = x(12.5 - x) = 12.5x - x^2.

Finding the derivative:

dA /dx = 12.5 - 2x

For a maximum area this = zero

12.5 - 2x = 0

x = 6.25m.

and w = 25 - 12.5 = 6.25m.

(For any rectangle the maximum area is always a square).

Answer 2

Square with side length 25/4 m

Explanation:

The area is always going to be largest for a rectangle when the two dimensions are equal. You are looking for a square. What square has perimeter 25? 4s=25 so the side length of this rectangle (Square) is 25/4 m.