Question

given triangle ABC ~ triangle PQR AB/PQ =1/3 then find the area of triangle ABC/ triangle PQE

Answer 1

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Given that

=> ∆ABC ~ ∆PQR

=> AB = 1/ 3 PQ

We know that

Ratio of Areas of two similar triangles is equal to the ratio of the squares of their corresponding side

$= > \frac{ar \: (abc)}{ar(abc)} = {( \frac{ab}{pq} )}^{2} \\ \\ = > {( \frac{1}{3} )}^{2} \\ \\ = > \frac{1}{9} < = = = answer \\ \\ i \: hope \: it \: will \: help \: you \: \\ \\ thanks \: \\ \\ have \: \: a \: nice \: day$


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Answer 2

Given:

ABC and PQR are similar triangles.

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

To find:

The ratio of area of triangle ABC and area of triangle PQR

Solution:

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

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

$\frac{{area}(A B C)}{{area}(P Q R)}=\left(\frac{A B}{P Q}\right)^{2}=\left(\frac{B C}{Q R}\right)^{2}=\left(\frac{A C}{P R}\right)^{2}$

$\frac{{area}(A B C)}{{area}(P Q R)}=\left(\frac{1}{3}\right)^{2}$

$\frac{{area}(A B C)}{{area}(P Q R)}=\frac{1}{9}$

The ratio of area of triangle ABC and triangle PQR is $\frac{1}{9}$.

To learn more...

1. Given ABC~ PQR, if AB/PQ=1/3,then find ar ABC/ar PQR

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2. In triangle ABC,PQ is a line segment intersecting AB at P and AC at Q such that PQllBC and PQ divides triangle ABC into two parts in equal area.Find BP/AB.

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