Question

How many different kinds of rectangles can you make with the perimeter of 24cm? Find the area of each rectangle. Write your conclusion.

Answer 1

the area of rectangle 48

Answer 2

If a and b are the sides of the rectangle then the perimeter is 2a+2b. You are given a string 24 cm long (which will be the perimeter) from which to make the rectangles. So,

2a + 2b = 24

2(a + b) = 24

a + b = 12

If the sides must be integers, then the possibilities are:

a = 1, b = 11

a = 2, b = 10

a = 3, b = 9

a = 4, b = 8

a = 5, b = 7

a = 6, b = 6

If a=7, then b=5 which is the same as the fifth rectangle listed, i.e., a=5, b=7.

So there are only 6 possible rectangles (the square a=6 & b=6, being a special case of a rectangle).