Two regular decagons have areas of 30 mm² and x² + 7x mm². What values of x make the decagons congruent?

Question

apoorvk · Answer

Since the areas are equal, equate the expressions for both areas:
$$30 = x^2 + 7x$$

Now, bring every term to the same side, and lo! you have a quadratic. solve it, find 'x' and enjoy!

foolaroundmath · Answer

Two polygons are congruent if they are exactly the same.

What can you say about the area of two congruent polygons?

ledah · Answer

They should also be the same

foolaroundmath · Answer

So, all you have to do is equate their areas and get a quadratic equation as obtained by @apoorvk and solve it.

ledah · Answer

I got 5 and -6 as an answer..
I'm not sure if its right I'm still checking my work

apoorvk · Answer

Umm, sorry that isn't correct - did you split the middle term and factorize it?

foolaroundmath · Answer

$x=5$ does not satisfy the equation.
What you have is $x^{2}+7x-30 = 0$

Can you factorise the left hand side?