Math without Numbers (2)

Geometry Level 3

Suppose m \color{#D61F06} m and n \color{#20A900}n are positive integers where m > n \color{#D61F06}m\color{#333333}>\color{#20A900}n .

Then the perimeter of a rectangle constructed from m \color{#D61F06}m squares of side length s \color{#3D99F6}s is greater than the perimeter of a rectangle constructed from n \color{#20A900}n squares of side length s \color{#3D99F6}s .

Is the above statement True or False?

False True

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1 solution

Marta Reece
Jul 9, 2017

To prove a proposition is false, a single counterexample is sufficient. Here the perimeter of a figure made of 6 unit squares is 2 ( 2 + 3 ) = 10 2(2+3)=10 , while perimeter of a rectangle made of only 5 unit squares is 2 ( 1 + 5 ) = 12 2(1+5)=12 .

Thank you for sharing a nice solution.

Hana Wehbi - 3 years, 11 months ago

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