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

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.