Math without Numbers (2)

Geometry Level 3

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

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

Is the above statement True or False?

False True

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 $2(2+3)=10$ , while perimeter of a rectangle made of only 5 unit squares is $2(1+5)=12$ .

Thank you for sharing a nice solution.

Hana Wehbi - 3 years, 11 months ago

Math without Numbers (2)

1 solution

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