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(B) 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 thei

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(B) 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.Let the areas of the two triangles be $A_1 = 144$ and $A_2 = 81$.Let the corresponding longest sides be $s_1 = 36$ and $s_2 = x$.According to the theorem: $\frac{A_1}{A_2} = (\frac{s_1}{s_2})^2$.Substituting the values: $\frac{144}{81} = (\frac{36}{x})^2$.Taking the square root on both sides: $\sqrt{\frac{144}{81}} = \frac{36}{x}$.This simplifies to: $\frac{12}{9} = \frac{36}{x}$.Further simplifying the fraction: $\frac{4}{3} = \frac{36}{x}$.Cross-multiplying gives: $4x = 36 	imes 3$.$4x = 108$.$x = \frac{108}{4} = 27$.Therefore,the length of the longest side of the second triangle is $27$.

The areas of two similar triangles are $144$ and $81$. If the length of the longest side of the first triangle is $36$,the length of the longest side of the second triangle is........

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