Question : $\Delta ABC$ and $\Delta DEF$ are two similar triangles and the perimeters of $\Delta ABC$ and $\Delta DEF$ are 90 cm and 54 cm respectively. If the length of DE = 36 cm, then the length of AB is:
Option 1: 60 cm
Option 2: 40 cm
Option 3: 45 cm
Option 4: 50 cm
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Correct Answer: 60 cm
Solution :
The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.
$\frac{{AB}}{DE} = \frac{\text{Perimeter of $\Delta ABC$}}{\text{Perimeter of $\Delta DEF$}}$
⇒ $\frac{AB}{36\;cm} = \frac{90\;cm}{54\;cm}$
⇒ AB = 60 cm
Hence, the correct answer is 60 cm.
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