Mathematics, 29.06.2019 10:00 yessijessiHaley
The shortest side of a polygon of area 196 in² is 4" long find the area of similar polygon who shortest side is 8" long
Answers: 1
![\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill](/tpl/images/0030/5899/a310b.png)
![\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}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{sides}{\cfrac{4^2}{8^2}}=\stackrel{Areas}{\cfrac{196}{a}}\implies \cfrac{16}{64}=\cfrac{196}{a}\implies \cfrac{1}{4}=\cfrac{196}{a}\implies a=784](/tpl/images/0030/5899/0b2be.png)
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