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

Answer 1

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

Answer 2

48 = x^2 + 8x

Answer 3

x^2 + 8x -48 = 0

Answer 4

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

Answer 5

x= -12 and x= 4?

Answer 6

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.

Answer 7

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