Question : If $\triangle$ABC ~ $\triangle$DEF such that 2AB = DE and BC = 8 cm, then the length of EF is:
Option 1: 16 cm
Option 2: 18 cm
Option 3: 22 cm
Option 4: 20 cm
Correct Answer: 16 cm
Solution :
Given: △ABC∼△DEF, such that 2AB = DE and BC = 8 cm.
If two triangles are similar then their corresponding sides are proportional.
⇒ $\frac{\text{EF}}{\text{BC}}=\frac{\text{DE}}{\text{AB}}$
⇒ $\frac{\text{EF}}{8}=\frac{2\text{AB}}{\text{AB}}$
⇒ $\text{EF}=2×8$
⇒ $\text{EF}=16$ cm
Hence, the correct answer is 16 cm.
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