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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