Question

Ratio of areas of two similar triangles is 9 : 25. _______ is the ratio of their corresponding sides.

विकल्प

• 3 : 4

• 3 : 5

• 5 : 3

• 25 : 81

Answer 1

3: 5

Let ΔABC and ΔPQR be two similar triangles.  

According to the given condition,

${\displaystyle \frac{\text{A(ΔABC)}}{\text{A(ΔPQR)}}=\frac{9}{25}}$      ...(Given)

But ${\displaystyle \frac{\text{A(ΔABC)}}{\text{A(ΔPQR)}}=\frac{{\text{AB}}^2}{{\text{PQ}}^2}}$ ...(By the theorem of areas of similar triangles)

∴ ${\displaystyle \frac{{\text{AB}}^2}{{\text{PQ}}^2}=\frac{9}{25}}$

∴ ${\displaystyle \frac{\text{AB}}{\text{PQ}}=\frac{3}{5}}$

∴ 3: 5 is the ratio of their corresponding sides.