Two regular pentagons have areas of 20 mm² and x² - x mm². What values of x make the pentagons congruent?

Answer

5 and - 4

Explanation

If the two triangle are congruent then they have the same area.

20 = x² - x

x² - x - 20 = 0

x² - x + (1/2) ² = 20 + (1/2) ²

(x - 1/2) ² = 20.25

x - 1/2 = √20.25

x - 1/2 = 4.5 or x - 1/2 = - 4.5

x = 4 1/2 + 1/2 x = - 4 1/2 + 1/2

= 5 = - 4

The values of x are 5 and - 4.