The perimeter of a rectangle is 20 cm20cm. What are the possible dimensions if the area must be less than 21 cm^221cm2?cm^2?

1 Answer
Mar 19, 2018

(a, b) = (5, 5), (4,6), (3, 7), (2,8), (1,9), (6,4),(7,3),(8,2),(9,1)(a,b)=(5,5),(4,6),(3,7),(2,8),(1,9),(6,4),(7,3),(8,2),(9,1)

Explanation:

Let's analyze. So perimeter of a rectangle is given by the formula:
P = 2*(a+b)P=2(a+b).
So, 2 * ( a+b) = 202(a+b)=20
And we are given that Area < 21cm^2cm2 => a*b < 21ab<21
Back to perimter, 2*(a+b) = 202(a+b)=20 => a+b = 20/2 = 10a+b=202=10
And we are given a*b < 21ab<21, which gives us pairs
(a, b) = (5, 5), (4,6), (3, 7), (2,8), (1,9), (6,4),(7,3),(8,2),(9,1)(a,b)=(5,5),(4,6),(3,7),(2,8),(1,9),(6,4),(7,3),(8,2),(9,1)