Question

The area of a rectangle is 18 square centimeters. If the length and width are whole numbers, what are the least and greatest possible perimeters.

18 cm and 38 cm
1 cm and 18 cm
18 cm and 36 cm
19 cm and 9 cm

Answer 1

The clue is in the "whole numbers"

You are looking at whole numbers whose product is 18.
1x18
2x9
3x6

P 1 = 2+ 36 = 38
P2 = 4+18 = 22
P3 = 6+12 = 18

P1 Max perimeter
P3 minimum

Answer 2

option(a)

Explanation:

Area of Rectangle= Length × Breadth

It is given that area of rectangle 18 square centimeters

So, the possible values of length breadth are

18= 1×19

18=2×9

18=3×6

By considering first, l=1 , b= 19

Perimeter of rectangle= 2(l+b)

Perimeter= 2(1+18)

Perimeter= 2×19= 38 centimeter

By considering second, l=2, b= 9

Perimeter of rectangle= 2(l+b)

Perimeter= 2(2+9)

Perimeter= 2×11= 22 centimeter

By considering third, l=3 , b= 6

Perimeter of rectangle= 2(l+b)

Perimeter= 2(3+6)

Perimeter= 2×9= 18 centimeter

Hence, least possible perimeter= 18 cm, greatest possible perimeter 38 cm

Hence option(a) is correct