Question

ΔQRS~ΔXYZ, QR=9, RS=12, QS=14, and YZ=18, then the scale factor of ΔQRS to ΔXYZ is....

Answer 1

⇒ Since ΔQRS~ΔXYZ,

so XY/QR = YZ/RS = XZ/QS = P2/P1   = k

P2 = Perimeter of ΔXYZ,

P1 = Perimeter of ΔQRS

k = Scale factor of ΔXYZ to ΔQRS

QR=9, RS=12, QS=14, and YZ=18,

Let the scale factor be "k"

P1 = QR+RS+QS = 9+12+14 = 35

P2 = XY+YZ+ZX = XY+18+ZX

But XY/9 = 18/12 = ZX/14 = P2/35 = k

so XY = 9k, ZX = 14k

As P2 = kP1

so XY+18+ZX = 35k

9k+18+14k = 35k

i.e 23k+18 = 35k

or k = 18/12

and k = 3/2

So scale factor K  ΔQRS to ΔXYZ is 1/k = 2/3