Question

the sides of a similar triangle are in the ratio 3:4 then their areas are in the ratio?​

Answer 1

Answer:

Step-by-step explanation:

Let the two triangles be ABC and DEF

Since the triangles are similar by using areas of similar triangles theorem we can say:

→ ar(ABC)/ar(DEF) = AB²/DE²

→ ar(ABC)/ar(DEF) = (3)²/(4)²

→ ar(ABC)/ar(DEF) = 9/16

Hence,

→Sides of two triangles are in the ratio 3:4 find the ratio of their areas is 9:16

Answer 2

Answer is 9/16

Now,

Consider :

Triangle ABC and Triangle DEF are similar to each other.

Therefore,

$\frac{ab}{de} = \frac{bc}{ef} = \frac{ca}{fd}$

Now,

We know that :-

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



Now,

The ratio of the corresponding sides of the similar triangles is given as 3:4

So,

The ratio of their areas will be :-

$\frac{ {3}^{2} }{ {4}^{2} } = \frac{9}{16} \\ \\ \\ 9 : 16$