Question : The perimeter of two similar triangles RST and IJK (in correspondence) is 56 cm and 64 cm respectively. If IJ = 16 cm, then what is the length of RS?
Option 1: 18 cm
Option 2: 16 cm
Option 3: 14 cm
Option 4: 8 cm
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Correct Answer: 14 cm
Solution :
In similar triangles, the ratio of their corresponding sides is equal to the ratio of their perimeters.
Given that the perimeters of triangles RST and IJK are 56 cm and 64 cm respectively, the ratio of their perimeters is:
$\frac{\text{Perimeter of RST}}{\text{Perimeter of IJK}} = \frac{\text{RS}}{\text{IJ}}$
⇒ $\frac{56}{64} = \frac{\text{RS}}{16} $
⇒ RS = 14 cm
Hence, the correct answer is 14 cm.
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