MATH SOLVE

4 months ago

Q:
# If the ratio of areas of two similar polygons is 25:49, what is the ratio of the corresponding side lengths

Accepted Solution

A:

[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \stackrel{\textit{ratio of sides}}{\cfrac{s}{s}}=\stackrel{\textit{ratio of the areas}}{\cfrac{\sqrt{s^2}}{\sqrt{s^2}}}\implies \cfrac{s}{s}=\cfrac{\sqrt{25}}{\sqrt{49}}\implies \cfrac{s}{s}=\cfrac{5}{7}[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \stackrel{\textit{ratio of sides}}{\cfrac{s}{s}}=\stackrel{\textit{ratio of the areas}}{\cfrac{\sqrt{s^2}}{\sqrt{s^2}}}\implies \cfrac{s}{s}=\cfrac{\sqrt{25}}{\sqrt{49}}\implies \cfrac{s}{s}=\cfrac{5}{7}[/tex]