Delta XYZ sim Delta DEF for the correspondenc | vedclass

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(C) The correspondence $XYZ \leftrightarrow EFD$ indicates that the triangles are similar.According to the theorem of areas of similar triangles,the r

Vedclass · Accepted Answer

$40.5$

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(C) The correspondence $XYZ \leftrightarrow EFD$ indicates that the triangles are similar.According to the theorem of areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.$	herefore \frac{	ext{Area}(\Delta XYZ)}{	ext{Area}(\Delta DEF)} = \left(\frac{XY}{EF}ight)^2$Given that $	ext{Area}(\Delta XYZ) = 18$ and $\frac{XY}{EF} = \frac{2}{3}$.Substituting these values into the formula:$\frac{18}{	ext{Area}(\Delta DEF)} = \left(\frac{2}{3}ight)^2$$\frac{18}{	ext{Area}(\Delta DEF)} = \frac{4}{9}$$	ext{Area}(\Delta DEF) = \frac{18 	imes 9}{4}$$	ext{Area}(\Delta DEF) = \frac{162}{4} = 40.5$

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EFD$. If $XY : EF = 2 : 3$ and the area of $\Delta XYZ$ is $18$,then the area of $\Delta DEF$ is........

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