Answer: In ΔXYZ, XY = 7.5 cm, ∠XYZ = 40°, YZ = 9.5 cm.
Analysis: \(\dfrac{RS}{XY}=\dfrac{ST}{YZ}=\dfrac35\) and \(\angle S = \angle Y = 40^\circ\).
\(XY = 4.5\times\tfrac53 = 7.5\) cm, \(YZ = 5.7\times\tfrac53 = 9.5\) cm. ΔXYZ is bigger.
Steps of construction:
- Draw seg ST = 5.7 cm. At S draw ray making \(\angle TSR = 40^\circ\); on it mark R with SR = 4.5 cm. Join RT. This is ΔRST.
- Draw seg YZ = 9.5 cm. At Y draw ray making \(\angle ZYX = 40^\circ\); on it mark X with YX = 7.5 cm. Join XZ. This is ΔXYZ.
(Alternatively, keep S and Y together: extend SR and ST, divide a ray from S into 5 equal parts, join \(S_3T\), draw a parallel through \(S_5\) to get Z on ray ST, then through Z draw a parallel to TR to get X on ray SR.)