Question

the figures below are similar. the labeled sides are corresponding. what is the perimeter of the smaller square?

Answer 1

Pairs of similar figures have a constant ratio in all its length measures.

Perimeter is a type of length, and the measures of sides are too.

From the given sides, we can calculate this ratio:

$r=\frac{3.9}{3.8}$

Now, we can use this ratio to calculate the missing perimeter:

$\begin{gathered} r=\frac{P_2}{P_1} \\ P_1=\frac{P_2}{r}=\frac{15.6}{(\frac{3.9}{3.8})}=15.6\cdot\frac{3.8}{3.9}=15.2 \end{gathered}$

So, the perimeter is:

$P_1=15.2in$