Answer:
The perimeter of B is 153 cm.
Explanation:
Given two similar shapes and:
• The internal diameter of A = 6 cm
,
• The internal diameter of B = 18 cm
The ratio of the perimeters of two similar shapes is equal to the ratio of the length of corresponding sides.
[tex]\begin{gathered} \frac{\text{ Internal Diameter of A}}{\text{ Internal Diameter of B}}=\frac{\text{ Perimeter of A}}{\text{ Perimeter of B}} \\ \frac{6}{18}=\frac{51}{\text{ Perimeter of B}} \end{gathered}[/tex]
We solve for the perimeter of B.
[tex]\begin{gathered} \frac{6}{6\times3}=\frac{51}{x} \\ \frac{1}{3}=\frac{51}{x} \\ x=51\times3 \\ x=153\text{ cm} \end{gathered}[/tex]
The perimeter of B is 153 cm.
