Question

how many rectangles of perimeter 36cm can be made if the sides in cm of the rectangle are odd

Answer 1

Perimeter = 38 
⇒ 2 ( l + w ) = 38 
⇒ l + w = 19  
Since length and width are positive integers in centimeters. Therefore, possible dimensions are : 
( 1, 18 )cm , ( 2, 17 ) cm , ( 3, 16 ) cm, (4 , 15) cm, ( 5,14) cm, ( 6, 13) cm , ( 7, 12) cm, ( 8, 11 ) cm, ( 9, 10) cm.  
Hence, there are 9 rectangles.

Answer 2

There are 5 possibilities.

Step-by-step explanation:

Let the length and width of the rectangle are L cm and W cm respectively.

So, the perimeter P = 2(L + W) = 36 cm (Given)

⇒ L + W = 18 cm ........... (1)

Now, we have to select the odd value of L and W for which equation (1) will be satisfied.

So, L = 1, 3, 5, 7, and 9 are the possible values of L and the corresponding W values are W = 17, 15, 13, 11, and 9.

Therefore, the dimensions of the rectangles will be (1 cm by 17 cm), (3 cm by 15 cm), (5 cm by 13 cm), (7 cm by 11 cm) and (9 cm by 9 cm).

So, there are 5 possibilities. (Answer)