Question

How many rectangles can be drawn with 36 cm as the perimeter, given that lengths of sides are in positive integers in cm

Answer 1

17&1

16&2

15&3

14&4

13&5

12&6

11&7

10&8

9&9

8&10

7&11

6&12

5&13

4&14

3&15

2&16

1&17

Answer 2

Answer:

• Perimeter = 36

• ⇒ 2 ( l + w ) = 36

• ⇒ l + w = 18

Since length and width are positive integers in centimeters. Therefore, possible dimensions are

:

• ( 1, 17 )cm , ( 2, 16 ) cm , ( 3, 15 ) cm, (4 , 14) cm, ( 5,13) cm, ( 6, 12) cm , ( 7, 11) cm, ( 8, 10 ) cm, ( 9, 9) cm.

• Hence, there are 9 rectangles.

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