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

Explanation:

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.