Question

If ΔPQR ~ ΔLMN, 9 × A(ΔPQR) = 16 × A(ΔLMN) and QR = 20, then find MN.

Answer 1

9 × A(△ PQR) = 16 × A(△ LMN)

∴ `(A(Delta PQR))/(A(DeltaLMN)) = 16/9`     ...(1)

△ PQR ∼ △ LMN              ...(Given)

`(A(Delta PQR))/(A(DeltaLMN)) = (QR^2)/(MN^2)`      ...(Theorem of areas of similar triangles)

∴ `16/9 = ((20)^2)/(MN^2)`       ...[From (1) and given]

∴ `4/3 = 20/(MN)`        ...(Taking square roots of both the sides)

∴ MN = `(20 xx 3)/4`

MN = 15