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?

1 Answer
Elvin Jafarli
Mar 19, 2018

#(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)#

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