What's around the area of Royal Holloway?

The perimeter of a rectangle is 18cm. whats its greatest possible area?area of rectangle 36cm2 least perimeter

• the area of a rectangle is 18cm whats its greatest possible area? another ? ummm...the area of a rectangle is 36cm2 whats its least possible perimeter? SMART PEOPLE HELP ME PLZ!!!! I WILL LOVE YOU FOR EVER!!! Email me if you want 2 talk

• Answer:

  For the first, if one side is x, then another side would be 9-x (so that they would add up to 18). The area is then A = x(9-x) = 9x - x^2 To find the maximum area, take the first derivative and set it to 0: A' = 9 - 2x 0 = 9 - 2x 2x = 9 x = 9/2 Since the parabola opens down, the maximum area happens when x = 9/2. So if x = 9/2, the other side is 9 - 9/2, or 9/2 - it turns out to be a perfect square! And the area is then (9/2)^2, or 81/4. For the second, you already have an area and you need to find the perimeter. So, lw = 36, and we're trying to find the smallest 2l + 2w. Well, l = 36/w, so the perimeter can be expressed as P = 2l + 2w = 2(36/w) + 2w = 72/w + 2w We can take a derivative and set it to 0 to find the minimum value here: P' = -72/w^2 + 2 0 = -72/w^2 + 2 72/w^2 = 2 w^2 = 36 w = 6 So if w = 6, then l = 6 as well, and the perimeter would then be 24.