Question

Given triangle ABC ~ triangle PQR if AB/PQ=1/3 then find area of triangle ABC / triangle PQR

Answer 1

Since the area of two similar triangles are equal to the ratio of their corresponding sides therefore area abc/area pqr= ab ^2/pq ^2
=(1/3)^2
=1/9
hence ar. ABC/ar. PQR=1/9

Answer 2

Answer:

The ratio of area of triangle ABC and PQR is 1:9.

Step-by-step explanation:

Given information: triangle ABC ~ triangle PQR,

If two triangles are similar, the their corresponding sides are proportional.

It is given that

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

Let the side AB be x and PQ is 3x.

$\frac{A(\triangle ABC)}{A(\triangle PQR)}}=\frac{(AB)^2}{(PQ)^2}$

$\frac{A(\triangle ABC)}{A(\triangle PQR)}}=\frac{(x)^2}{(3x)^2}$

$\frac{A(\triangle ABC)}{A(\triangle PQR)}}=\frac{(x)^2}{9x^2}$

Cancel out the common factor.

$\frac{A(\triangle ABC)}{A(\triangle PQR)}}=\frac{1}{9}$

Therefore the ratio of area of triangle ABC and PQR is 1:9.