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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
Solution
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.
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