Math Is Fun Forum

balasvce

Member

Registered: 2006-12-20

Posts: 37

solve

36) area of rectangle with perimeter 10 and area of circle

with radius 10
column a:area of rectangle
col b:area of circle
compare which is greater

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: solve

The area of a circle is always

.  So for a circle of radius 10, the area is

or 314.159268

The area of a rectangle is height * width.   But you don't know the height or the width, only the perimeter.   There is no limit to the number of rectangles with a perimeter of 10.  The rectangle could have height and width of 1 and 4 (1+1+4+4=10) or 1.5 and 3.5 (1.5+1.5+3.5+3.5=10) and so on.   

Since your questions doesn't specify any more details about the height and width, I'm only going to so solutions where both of them are integers. 

Length    Width    Perimeter   Area
    1           4            10          4
    2           3            10          6
    3           2            10          6
    4           1            10          4