Question

If ∆XYZ ~ ∆PQR and A(∆XYZ) = 25 cm², A(∆PQR) = 4 cm² then XY : PQ = ?

Options

• 4 : 25

• 2 : 5

• 5 : 2

• 25 : 4

Answer 1

5 : 2

Explanation:

In ∆XYZ and ∆PQR,

∆XYZ ~ ∆PQR  

A(∆XYZ) = 25 cm², A(∆PQR) = 4 cm²   ...(Given)

By the theorem of areas of similar triangles,

`(A(∆XYZ))/(A(∆PQR)) = (XY^2)/(PQ^2)`

∴ `25/4 = (XY^2)/(PQ^2)`

∴ `(XY)/(PQ) = 5/2`

∴ XY : PQ = 5 : 2.