Please answer the question in the picturee

Mathematics

1 answer:

marin [14]3 years ago

6 0

Answer: 8

Step-by-step explanation:

12-4= 8

*8 is the length of the side because of this theory I forgot, but yeah!

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A rectangle has an area of 20 ft.² in a similar rectangle has an area of 180 ft.² what is the ratio of areas of the similar

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$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------\\\\$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s^2}{s^2}=\cfrac{20}{180}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{20}{180}\implies \cfrac{s}{s}=\sqrt{\cfrac{20}{180}}
\\\\\\
\cfrac{s}{s}=\cfrac{\sqrt{20}}{\sqrt{180}}\implies \cfrac{s}{s}=\cfrac{2\sqrt{5}}{6\sqrt{5}}\implies \cfrac{s}{s}=\cfrac{2}{6}\implies \cfrac{s}{s}=\cfrac{1}{3}$

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