“Impossible” perimeter problem

Geometry Tutorial

"Impossible" perimeter problem

Intro

Seemingly complex, but actually rather simple problem involving perimeter

Sample Problem

Question source

Perimeter problem

Solution

solution

The first one can be calculated as follows, a+b+c+d+e+f = a+(b+c)+(d+e)+f = a+f+a+f
= 12+10+12+10 = 44, where you can see that the sum of sides b and c is equivalent to side f, and the sum of sides d and e is equivalent to side a

The second one can be calculated in a similar manner. Here it gets a little complicated though, as the shape overlaps itself a little bit. The 2cm corresponds to the lengths highlighted in red which are overlapping bits in the regular rectangle

a+b+c+d+e+f+g = a+b+(c+d+e)+(f+g)+2+2 = a+b+a+b+2+2 = 9+11+9+11+2+2 = 44.



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