Question

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

Answer 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)`.
So, `2 * ( a+b) = 20`
And we are given that Area < 21`cm^2` `=>` `a*b < 21`
Back to perimter, `2*(a+b) = 20` `=>` `a+b = 20/2 = 10`
And we are given `a*b < 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)`