The areas of two similar triangles are 9 and | vedclass

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(A) 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

$3:4$

Vedclass · Answer

(A) 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 $A_1 = 9$ and $A_2 = 16$.Let the corresponding sides be $s_1$ and $s_2$.Therefore,$\frac{A_1}{A_2} = (\frac{s_1}{s_2})^2$.Substituting the given values: $\frac{9}{16} = (\frac{s_1}{s_2})^2$.Taking the square root on both sides: $\sqrt{\frac{9}{16}} = \frac{s_1}{s_2}$.Thus,$\frac{s_1}{s_2} = \frac{3}{4}$.The ratio of their corresponding sides is $3:4$.

The areas of two similar triangles are $9$ and $16$. Then,the ratio of their corresponding sides is...............

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