Question

The area of a rectangle is 36 sq.cm.What is the minimum perimeter this figure can have if the sides are natural numbers in cm?

Answer 1

area of a rectangle = 36 sq cm

to have area as 36 sq cm with natural numbers for length and breadth

possible solutions are

1× 36 , 2 ×18 , 3×12 , 4×9, 6×6

also its known very well that square will have minimum perimeter and square is also one of rectangle

so perimeter = 2× (6+6) = 24 cm

also if we calculate perimeters i each case

4×9 = 2 ×(4+9) = 26 cm

3×12 = 2 ×(3+12) = 30 cm

2 × 18 = 2 × (2 + 18) = 40 cm

1 × 36 = 2 × (1+36) = 74 cm

minimum perimeter = 24 cm

if we do not want to consider square then minimum perimeter = 26cm