Two similar triangles. One area is 56 cm^2 and the other is 343 cm^2...on side of the first triangle is 8...whats the length of the corresponding side?
In similar figurs the ratio of the areas is the square of the ratio of corresponding linear dimensions.
Here the ratio of the areas is $\displaystyle 56/343$ and so if $\displaystyle s$ is the unknown corresponding side of the second triangle:
$\displaystyle
56/343 = (8/s)^2
$
RonL