Question

जर ∆ ABC ~∆ PQR आणि AB : P Q = 4.5 तर A(∆ ABC) A(∆ PQR) = किती ?​

Answer 1

We need to recall the following property for similar triangles.

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

This problem is about the area theorem of similar triangles.

Given:

ΔABC ~ ΔPQR

$\frac{AB}{PQ}=\frac{4}{5}$

From the area theorem, we get

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

$\frac{A(ABC)}{A(PRQ}=\frac{4^2}{5^2}$

$\frac{A(ABC)}{A(PRQ}=\frac{16}{25}$

Hence, the ratio of the areas of similar triangles is $\frac{16}{25}$

Answer 2

We must recall that:

If we have two similar triangles, then not only their angles and sides share a relationship but also the ratio of their perimeter, altitudes, angle bisectors, areas and other aspects are in ratio.

Given: $\frac{AB}{PQ}=\frac{4}{5}$

Area $\frac{\triangle ABC}{\triangle PQR}=(\frac{AB}{PQ})^2=\frac{16}{25}$

Hence $\frac{\triangle ABC}{\triangle PQR}=\frac{16}{25}$