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.

Related questions
See all questions in Perimeter and Area of Non-Standard Shapes
Impact of this question
11484 views around the world
You can reuse this answer
Creative Commons License