Question

If the corresponding sides of two similar triangles are in the ration 4:9 then the areas of these triangles are in the ratio?

Answer 1

Answer:

16:81

Step-by-step explanation:

If sides of two similar triangles are in the ratio a:b, their areas are in the proportion a2:b2

As in given case sides are in the ratio of 4:9.

ratio of their areas is 4^2:9^2 or 16:81

Answer 2

Step-by-step explanation:

Theorem :-

The ratio of the areas of two similar triangles is equal to square of the ratio of corresponding sides.

GIVEN THAT:-

If the corresponding sides of two similar triangles are in the ration 4:9 then the areas of these triangles are in the ratio?

ANSWER

Ratio we have as 4:9. Let ratio be x.

And by the above theorem, we can state that

$\frac{ ({4x})^{2} }{( {9x})^{2} } = \frac{ratio \: of \: first \: triangle}{ratio \: of \: second \: triangle}$

So we have it as

$\frac{(16 {x}^{2}) }{(81 {x}^{2}) }$

Where x² and x² gets cancelled.

So,

We have the ratio as 16/81.