Question

If \(\Delta ABC\) and \(\Delta DEF\) are similar such that \(2 AB = DE\) and \(BC = 8\) cm, then \(EF\) is equal to :

• A. 4 cm
• B. 8 cm
• C. 12 cm
• D. 16 cm

Hint:

Similarity is about "scaling". If \(DE\) is twice \(AB\), then every side of \(\Delta DEF\) is twice the corresponding side of \(\Delta ABC\). So \(EF = 2 \times BC\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When two triangles are similar (\(\Delta ABC \sim \Delta DEF\)), the ratios of their corresponding sides are equal.
Step 2: Key Formula or Approach:
\[ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \]
Step 3: Detailed Explanation:
Given that \(2 AB = DE\), we can write the ratio of corresponding sides as:
\[ \frac{AB}{DE} = \frac{1}{2} \]
Since the triangles are similar, the ratio of \(BC\) to \(EF\) must be the same:
\[ \frac{BC}{EF} = \frac{1}{2} \]
Substitute the given value \(BC = 8\) cm:
\[ \frac{8}{EF} = \frac{1}{2} \]
Cross-multiplying gives:
\[ EF = 8 \times 2 \]
\[ EF = 16 \text{ cm} \]
Step 4: Final Answer:
The length of \(EF\) is 16 cm.