MHB Solve Quadratic Equation: Ratio of Two Cones' Radii

[Monoxdifly]

Azis wants to make two cones using cartons. The surface area of the first cone is twice the second. The side length of the first cone is also twice the second. Determine the ratio of those cones' radius!

s1 = 2s2
L1 = 2L2
πr1(r1 + s1) = 2πr2(r2 + s2)
r1(r1 + 2s2) = 2r2(r2 + s2)

I was stuck with quadratic equations...

 

[skeeter]

Azis wants to make two cones using cartons. The surface area of the first cone is twice the second. The side length of the first cone is also twice the second. Determine the ratio of those cones' radius!

s1 = 2s2
L1 = 2L2
πr1(r1 + s1) = 2πr2(r2 + s2)
r1(r1 + 2s2) = 2r2(r2 + s2)

I was stuck with quadratic equations...

$A_1 = 2A_2 \implies \pi r_1 \cdot L_1 = 2\pi r_2 \cdot L_2 \implies \pi r_1 \cdot L_1 = 2\pi r_2 \cdot 2L_1 \implies \dfrac{r_1}{r_2} = 4$

 

[Monoxdifly]

But we must take into account the base area...