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

Answers

4 and

-12

Explanation

The octagons can be considered congruent when their areas are the same.

That is:

48 mm² = x² + 8x mm²

x² + 8x = 48

x² + 8x + 4² = 48 + 4²

(x + 4) ² = 48 + 16

= 64

x + 4 = √64 or x + 4 = - √64

x = 8 - 4 x = - 8 - 4

= 4 = - 12