Question

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

Options

• 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,

`"A(∆ABC)"/"A(∆PQR)" = ("AB"^2)/("PQ"^2)`

`"A(∆ABC)"/"A(∆PQR)" = 3^2/4^2`

`"A(∆ABC)"/"A(∆PQR)" = 9/16`.

∴ A(∆ABC) :  A(∆PQR) = 9 : 16.