Question

If triangle ABC~ triangle PQR , BC = 8 cm and QR = 6 cm, find the ratio of the areas of triangle ABC and triangle PQR.

Answer 1

the ratio of the areas of the similar triangle are in the ratio of the square of the corresponding sides
ar(∆ABC)/ar(∆PQR)=BC²/QR²
=8²/6²
=64/36
=16/9

Answer 2

Answer:

Ratio of area∆ABC and area ∆PQR = $\frac{16}{9}$

Step-by-step explanation:

By Theorem:

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

Here,

∆ABC ~ ∆PQR

BC = 8 cm,

QR = 6 cm

Ratio of area∆ABC and area ∆PQR

= Ratio of the squares of their corresponding sides

= $\frac{BC^{2}}{QR^{2}}$

= $\frac{8^{2}}{6^{2}}$

= $\frac{64}{36}$

= $\frac{16}{9}$

Therefore,

Ratio of area∆ABC and area ∆PQR = $\frac{16}{9}$

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