Question

sides of two Similar triangles are in the ratio 3:4. areas of these triangle are in the ratio?

Answer 1

Given:

The sides of two similar triangles are in the ratio 3:4

To be found:

The ratio of areas of these triangles

So,

Theorem - Areas of similar triangles can be used to find the ratio of the areas of the two similar triangle

The theorem says:

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

So,

If two triangles ABC and PQR are similar, i.e. ΔABC $\sim$ ΔPQR then,

$\boxed{\frac{ar(ABC)}{ar(PQR)}=(\frac{AB}{PQ})^{2} =(\frac{AC}{PR})^{2} =(\frac{BC}{QR})^{2}}$

So,

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

Hence,

The area of the two similar triangle whos side ratio is 3:4 is $\boxed{\boxed{\red{\sf{9:16}}}}$

$\underline{\sf{More\ Information:-}}$

• When the side ratio is given, do the square of the side ratio then we will get the ratio of the area of the similar triangles.
• And when the ratio of areas of two similar triangles would be given, then do the square root of the given ratio, and we will get the ratio of the sides of the similar triangle.

Answer 2

Given ,

• The ratio of sides of two similar triangle is 3 : 4

We know that ,

The ratio of areas of two similar triangle is equal to the square of their corresponding sides

So ,

The ratio of areas of two similar triangle will be

$\tt \implies { (\frac{3}{4}) }^{2}$

$\tt \implies \frac{9}{16}$

Hence , The ratio of areas of two similar triangle is 9 : 16