The areas of two similar triangles are 200 an | vedclass

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(D) For two similar triangles,the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.Let the areas be $A_1 = 20

Vedclass · Accepted Answer

$5:4$

Vedclass · Answer

(D) For two similar triangles,the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.Let the areas be $A_1 = 200$ and $A_2 = 128$.Let the corresponding altitudes be $h_1$ and $h_2$.According to the theorem,$\frac{A_1}{A_2} = \left(\frac{h_1}{h_2}\right)^2$.Substituting the values: $\frac{200}{128} = \left(\frac{h_1}{h_2}\right)^2$.Simplifying the fraction: $\frac{200}{128} = \frac{100}{64} = \frac{25}{16}$.Therefore,$\left(\frac{h_1}{h_2}\right)^2 = \frac{25}{16}$.Taking the square root on both sides: $\frac{h_1}{h_2} = \sqrt{\frac{25}{16}} = \frac{5}{4}$.Thus,the ratio of their corresponding altitudes is $5:4$.

The areas of two similar triangles are $200$ and $128$. Then,the ratio of their corresponding altitudes is.....

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