Question

A few squares are drawn in a sequence. The length of each side of the squares forms a geometric progression. The length of the side of the first square is x cm. The ratio of the length of the side of the third square to that of the first is 16:9 or sixteen to nine .
Find the ratio of the length of the side of the second square to that of the first square.

Answer 1

if the first side is \(x\) then the second side is \(xr\) and the third side is \(xr^2\)
you know that \(xr^2:x=16:9\) more clearly written as
\[\frac{xr^2}{x}=\frac{r^2}{1}=\frac{16}{9}\] telling you that \(r=\sqrt{\frac{16}{9}}=\frac{4}{3}\)