Question

if the ratio of corresponding medians of two similar triangles are 9:16 then find the ratio of their areas?

Answer 1

The ratio of the two similar area of the triangles are $81:256$

Explanation:

It is given that the ratio of corresponding medians of two similar triangles are $9:16$

We need to determine the ratio of their corresponding areas of the triangles.

Since, we know the theorem that, "the ratio of the areas of two triangles is equal to the square of the ratio of their corresponding medians".

Thus, we have,

$\frac{Area \ of \ 1st \ triangle}{Area \ of \ 2nd \ triangle} =(\frac{median \ of \ 1st \ triangle}{median \ of \ 2nd \ triangle})^2$

Substituting the medians, we get,

$\frac{Area \ of \ 1st \ triangle}{Area \ of \ 2nd \ triangle} =(\frac{9}{16})^2$

$\frac{Area \ of \ 1st \ triangle}{Area \ of \ 2nd \ triangle} =\frac{81}{256}$

Thus, the ratio of the areas of the two similar triangles is $81:256$

Learn more:

(1) The areas of two similar triangles are 144cm2 and 81cm2. if one median of the first triagle is 16cm,find the length of corresponding median of the second triangle.

brainly.in/question/2693211

(2) Sides of two similar triangles are in the ratio 4:9. find the ratio of areas of these triangles

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