Though you may use any numbers you wish each of these tasks

Though you may use any numbers you wish, each of these tasks can be performed with whole number dimensions that are less than or equal to 5. Draw two rectangles with the same area, but different perimeters. Draw two rectangles with the same perimeter, but different areas. Draw two rectangles in such a way that the first has a greater perimeter than the second, but the second has a greater area than the first. Draw two rectangular prisms with the same volume, but different surface areas. Draw two rectangular prisms in such a way that the first has a greater surface area than the second, but the second has a greater volume than the first.

Solution

1. Equal area but different perimeter

First : Length=2, Breadth=2, Area =4,Perimeter=2(2+2)=8

Second: Length=1,Breadth=4,Area=4,Perimeter=2(4+1)=10

2. Equal perimeter but different area

First: Length=2,Breadth=3,Area=2*3=6,Perimeter=2(2+3)=10

Second:Length=1,Breadth=4,Area=1*4=4,Perimeter=2(1+4)=10

3.

First: Length=8,Breadth=2, Area=16,Perimeter=2(8+2)=20

Second:Length=4,Length=9,Area=18,Perimeter=2(4+5)=18

4.

let rectangular prism have sides: length=a,breadth=b,width=c

Surface area of prism is: 2(ab+bc+ca)

We choose:c equal in both the prisms and only vary a and b

First prism: a=1,b=4,c=1 ,Volume=4, Surface area=2(4+4+1)=18

Second prism:a=2,b=2,c=1,Volume=4,Surface area=2(2+2+4)=16

5.

First prism: a=4,b=9,c=1 ,Volume=36, Surface area=2(4+9+36)=98

Second prism:a=8,b=2,c=3,Volume=48,Surface area=2(8*2+8*3+2*3)=92