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shtirl [24]
3 years ago
9

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

Mathematics
1 answer:
mihalych1998 [28]3 years ago
6 0
\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} \\\\
-----------------------------\\\\

\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}
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