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Question

(D) According to the theorem of the ratio of areas of two similar triangles,if $\Delta ABC \sim \Delta XZY$,then the ratio of their areas is equal to

Vedclass · Accepted Answer

$YZ^2$

Vedclass · Answer

(D) According to the theorem of the ratio of areas of two similar triangles,if $\Delta ABC \sim \Delta XZY$,then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.Specifically,$\frac{	ext{Area}(\Delta ABC)}{	ext{Area}(\Delta XZY)} = \frac{AB^2}{XZ^2} = \frac{BC^2}{ZY^2} = \frac{AC^2}{XY^2}$.Given the correspondence $ABC \leftrightarrow XZY$,the side $BC$ corresponds to the side $ZY$ (or $YZ$).Therefore,the ratio of the areas is $BC^2 : YZ^2$.Thus,the missing term is $YZ^2$.

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