Two regular octagons have areas of 48 mm² and x² + 8x mm². What values of x make the octagons congruent?
6 and 8
6 and -8
4 and 12
4 and -12

Question

Two regular octagons have areas of 48 mm² and x² + 8x mm². What values of x make the octagons congruent? 
   6 and 8 
 6 and -8 
 4 and 12 
 4 and -12

directrix · Answer

If two polygons are congruent, then they have equal areas.

directrix · Answer

48 = x^2 + 8x

directrix · Answer

x^2 + 8x -48 = 0

directrix · Answer

(x +12)(x-4) = 0
Zero Product Property
x + 12=0 or x-4 =0
x = ? or x = ?

anonymous · Answer

x= -12 and x= 4?

directrix · Answer

Yes. x is not a side of the polygon so there is no problem with the negative 12. When substituted in for x in x^2 + 8x, it cranks out a positve result.

anonymous · Answer

awesome thanks for all your help i can now understand and do them for myself now :)