Question

How many rectangles can be drawn with $32cm$ as the perimeter, given that the sides are positive integers in $cm$?

• A. 10
• B. 10
• C. 8
• D. 7

Answer 1

The correct option is C 8

Perimeter of rectangle $=2(l+b)$
$2(l+b)=32cm$
$(l+b)=16cm$
Since length and width are positive integers in centimeters. Therefore, possible dimensions are:
$(1,15),(2,14),(3,14),(4,12),(5,11),(6,10),(7,9),(8,8)$
So, we have $8$ possible rectangles.