Question

If ∆ABC ~ ∆PQR and AB : PQ = 3 : 4 then A(∆ABC) : A(∆PQR) = ?

पर्याय

• 9 : 25

• 9 : 16

• 16 : 9

• 25 : 9

Answer 1

9: 16

In ∆ABC and ∆PQR,

∆ABC ~ ∆PQR

AB : PQ = 3 : 4    ...(Given)

by theorem of areas of similar triangles,

${\displaystyle \frac{\text{A(∆ABC)}}{\text{A(∆PQR)}}=\frac{{\text{AB}}^2}{{\text{PQ}}^2}}$

${\displaystyle \frac{\text{A(∆ABC)}}{\text{A(∆PQR)}}=\frac{3^2}{4^2}}$

${\displaystyle \frac{\text{A(∆ABC)}}{\text{A(∆PQR)}}=\frac{9}{16}}$.

∴ A(∆ABC) :  A(∆PQR) = 9 : 16.