Delta ABC sim Delta XYZ for the correspondenc | vedclass

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Question

(C) Given that $\Delta ABC \sim \Delta XYZ$.According to the theorem of the ratio of areas of two similar triangles,the ratio of their areas is equal

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) Given that $\Delta ABC \sim \Delta XYZ$.According to the theorem of the ratio of areas of two similar triangles,the ratio of their areas is equal to the square of the ratio of their corresponding sides.Therefore,$\frac{	ext{Area}(\Delta ABC)}{	ext{Area}(\Delta XYZ)} = \left( \frac{AB}{XY} ight)^2$.Given $AB = 12$,$XY = 8$,and $	ext{Area}(\Delta ABC) = 81$.Substituting the values: $\frac{81}{	ext{Area}(\Delta XYZ)} = \left( \frac{12}{8} ight)^2$.Simplify the fraction: $\frac{12}{8} = \frac{3}{2}$.So,$\frac{81}{	ext{Area}(\Delta XYZ)} = \left( \frac{3}{2} ight)^2 = \frac{9}{4}$.Now,solve for $	ext{Area}(\Delta XYZ)$: $	ext{Area}(\Delta XYZ) = \frac{81 	imes 4}{9}$.$	ext{Area}(\Delta XYZ) = 9 	imes 4 = 36$.Thus,the area of $\Delta XYZ$ is $36$.

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB = 12, XY = 8$ and the area of $\Delta ABC$ is $81$,find the area of $\Delta XYZ$.

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