I think the "length of the triangle" you mean is rather "the length of its sides".
Assuming that this is so,
1. Use the ratio of the length of the sides as temporary length of the sides of the triangle. Then, use Heron's formula to find the area of the triangle using the ratio.
2. Solve for the actual length of the sides by taking advantage of the theorem of geometry that the ratio of the areas of two triangles is similar to the ratio of the length of the sides.
I hope this helps.