Problem 286
Consider the three following rectangles:
i
ii
iii
a. For each rectangle, determine the area (number of squares) and the perimeter (distance around).
b. What happens to the areas as you go from i to ii to iii?
c. What happens to the perimeters as you go from i to ii to iii ?
d. Write a statement that describes the connection between the perimeters and areas of these three rectangles.
Solution
a. (i) area = number of rows * number of square in a row
= 3*8 = 24
Perimeter = 3+8+3+8 = 22
(ii) area = 2*11 = 22
Perimeter = 2+11+2+11 = 26
(iii) area = 1*14 = 14
Perimeter = 1+14+1+14 = 30
b. Area decreases from (i) to (ii) and (ii) to (iii)
c. Perimeter increases from (i) to (ii) and (ii) to (iii)
d. The perimeters of all three stay about the same as the area of all three get smaller.