Question : The perimeter of two similar triangles GST and FAX are 48 cm and 36 cm, respectively. If FA = 12 cm, then GS is:
Option 1: 18 cm
Option 2: 16 cm
Option 3: 24 cm
Option 4: 12 cm
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Correct Answer: 16 cm
Solution :
Since the ratio of the corresponding sides of similar triangles is the same as the ratio of their perimeters. $\therefore \triangle$ GST~$\triangle$ FAX ⇒ $\frac{GS}{FA}=\frac{ST}{AX}=\frac{GT}{FX} = \frac{48}{36}$ ⇒ $\frac{GS}{12}= \frac{48}{36}$ $\therefore GS = 16\ \text{cm}$ Hence, the correct answer is 16 cm.
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