Question

Find the perimeter of thesimilar figure.8cm12cmPerimeter = 26cmPerimeter = [?]cm

Answer 1

2P = 39 cm

1) Since the first rectangle has a width of 8 cm and the perimeter (2P) of 26, and considering the side lengths we can write the following ratios:

`\begin{gathered} (side)/(2P)=\frac{side\text{ figure 2}}{2P_2} \\ (8)/(26)=(12)/(x) \\ 8x=12\cdot26 \\ 8x=312 \\ (8x)/(8)=(312)/(8) \\ x=39 \end{gathered}`

Note that we can state this relationship between two similar geometric figures. The side over the Perimeter = corresponding side/ Respective Perimeter.

2) Hence, the answer is 39 cm