Question

Q.12. Given ◇ ABC ~ ◇ PQR, if AB/PQ = 1/3, then ar (◇ ABC)/ ar (◇ PQR) = _________.
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Answer 1

Given:

ΔABC ~ ΔPQR

Also,

$\frac{AB}{PQ} = \frac{1}{3}$

To find:

$\boxed{\red{\frac{ar( \triangle ABC)}{ar(\triangle PQR)}=?}}$

Theorem:

Areas of similar triangle

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

So,

ΔABC ~ ΔPQR then

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

Now,

Given that $\frac{AB}{PQ} = \frac{1}{3}$

So,

$\bf \implies \frac{ar( \triangle ABC)}{ar(\triangle PQR)}=(\frac{AB}{PQ})^{2}$

$\bf \implies \frac{ar( \triangle ABC)}{ar(\triangle PQR)}=(\frac{1}{3})^{2}$

$\bf \implies \frac{ar( \triangle ABC)}{ar(\triangle PQR)}=\frac{1}{9}$

Hence,

$\boxed{\purple{\frac{ar( \triangle ABC)}{ar(\triangle PQR)}=\frac{1}{9}}}$

- - -

More Information:

• In two similar triangles, when the side ratio is given and the question is asking about the ratio of the areas of the similar triangle - Direct you do the square of the ratio of the side to get the answer. i.e. you will get the ratio of areas of the similar triangles.

• In two similar triangles, when the area of the similar triangles will be given and the question is asking to find the ratio of the sides then - direct you should do the square root of the ratio of the similar triangles, and you will get the required ratio of the sides.

Answer 2

Answer:

1/9 is your answer brother please mark