ABCDEF is an equiangular hexagon. The respective lengths of AB, BC, CD, DE, EF and FA are 10, 6, 12, 14, m and n

Find m and n.

Opposite sides are parallel.  To hold them parallel, the consecutive pair on one side must have the same sum as the consecutive pair on the other side.

AB || DE so 6+12=m+n
BC || EF so 12+14=n+10
CD || FA so 14+m=10+6

From which it follows m=2 and n=16

Interestingly although this gives 3 equations and is solvable for two unknowns (as long as they aren't parallel sides) it doesn't appear that it is solvable with any combination of three unknowns.

Posted by Jer on 2015-12-30 11:40:30