Respuesta :
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \stackrel{ratio}{\cfrac{3}{4}}\qquad \qquad \cfrac{3}{4}=\stackrel{areas}{\cfrac{\sqrt{a}}{\sqrt{100}}}\implies \cfrac{3}{4}=\cfrac{\sqrt{a}}{10}\implies 30=4\sqrt{a} \\\\\\ \cfrac{30}{4}=\sqrt{a}\implies \left( \cfrac{30}{4} \right)^2=a\implies \cfrac{900}{16}=a\implies \cfrac{225}{4}=a[/tex]
The area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Let's suppose the area of the smaller figure is x
Area of larger figure = 100 square units
The ratio of the areas:
= x/100
We also have:
Two similar figures have a side ratio of 3:4
= 3/4
Square it we will get ratio of the area
= 9/16
x/100 = 9/16
x = 900/16 = 225/4 or 56.25 square units
Thus, the area of the smaller figure is 225/4 or 56.25 square units if the two similar figures have a side ratio of 3:4.
Learn more about the ratio here:
brainly.com/question/13419413
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