Question

the sides of equilateral triangle angle XYZ And angle PQR are 12 cm and 8 cm respectively. the ratio of the areas of angle PQR and angle XYZ is​

Answer 1

Answer:

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.

ar (AABC) BC2 64 BC2 ar(AP QR) QR² 121 (15.4)²

8 11 BC 15.4

8 x 15.4 11 ⇒BC = = 11.2cm

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Answer 2

Given : the sides of equilateral triangle ΔXYZ and Δ PQR  are 12 cm and 8 cm respectively

To Find : ratio of the areas of  Δ PQR and  ΔXYZ  

Solution:

Note that all Equilateral triangles are similar to each other.

All the sides and angles of a equilateral triangle are equal

Equilateral triangles are similar as per AAA similarity

equilateral triangle ΔXYZ and Δ PQR

=>  ΔXYZ ~ Δ PQR  

Ratio of areas of similar triangle = ( ratio of corresponding sides)²

=> Ar ΔPQR / Ar ΔXYZ   =  ( PQ/XY)²

=> Ar ΔPQR / Ar ΔXYZ   =  (8/12)²

=> Ar ΔPQRZ / Ar ΔXYZ   =  ( 2/3)²

=> Ar ΔPQRZ / Ar ΔXYZ   =  4/9

ratio of the areas of Δ PQR and  ΔXYZ   is  4 : 9

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