Question

What is AB?

Answer 1

\(\Large a^2 = (b + c)c\)

Answer 2

@mathstudent55 I got an answer of -6.6 repeating. Which is pretty wrong, to say the least. What could I have done wrong?

Answer 3

@mathstudent55 you are wrong with the formula, with that drawing then the formula is
\[a ^{2}=b(b+c)\]
so with the sides a=8, b=x and c=12 then
\[8^{2}=x(x+12)\]
\[64=x ^{2}+12x\]
\[x ^{2}+12x-64=0\]
by factoring we get
\[(x+16)(x-4)=0\]
so possible solutions are x= -16 or x= 4, but x cannot be negative, so the only valid solution is x=AB=4

Answer 4

@Natriumhydrid Thank you so much!