The perimeter of a rectangle is 26 inches. If the inch-measure of each side is a natural number, how many different areas in square inches can the rectangle have?

1 Answer
Shwetank Mauria
Apr 22, 2018

Different area we can have are #12,22,30,36,40# and #42# square inches.

Explanation:

As perimeter is #26# inches, we have half the perimeter i.e. #"Length"+"Breadth"=13# inches.

As the inch-measure of each side is a natural number, we can have #"Length and Breadth"# as

#(1,12),(2,11),(3,10),(4,9),(5,8)# and #(6,7)#. (note that others are just repetition)

and hence different areas rectangle can have are #1xx12=12,2xx11=22,3xx10=30,4xx9=36,5xx8=40# and #6xx7=42# square inches.

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