Please help with my math!?

Question

Find the maximum area for the given perimeter of a rectangle. State the length and width of the rectangle.

1. 25mm

2.18yeards

3.42cm

Thanks so much and please tell me how you did it. :D

Answer 1

In order to do this, you have to know that to maximum the area of a rectangle you have to make it a square.

To make a square with a known perimeter of 25mm, you'd have a square with sides 25/4 mm. The area of this square would be (25/4)² = 39.0625 Square mm; The sides are 25/4cm or 6.25cm each.

To make a square with a known perimeter of 18 yards, you'd have a square with sides 18/4 yards. The area of this square would be (18/4)² = 20.25  Square yards. The sides are 18/4 or 4½ yards each.

To make a square with a known perimeter of 42cm, you'd have a square with sides 42/4cm. The area of this square would be (42/4)² = 110.25 Square cm. The sides are 42/4 or 10½ cm each.

Answer 2

1) The rectangle with the largest area to perimeter ratio is a Square.

25/4 is the side of the first square or rectangle.

So, it has area 625 / 16 mm^2

2) 18/4 = 9/2

9/2 ^2 = 81/4 yards^2

3) 42/4 = 21/2

21/2 ^2 = 441/4 cm^2