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

1 Answer

3 votes

Answers

4 and

-12


Step-by-step 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

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