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:

Always ensure you are matching the correct corresponding sides. In \(\Delta ABC \sim \Delta DEF\), \(BC\) corresponds to \(EF\), and \(AB\) corresponds to \(DE\).

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:
1. Given \(2 AB = DE\). This can be written as the ratio: \[ \frac{AB}{DE} = \frac{1}{2} \] 2. Since the triangles are similar, use the property of corresponding sides: \[ \frac{AB}{DE} = \frac{BC}{EF} \] 3. Substitute the known values (\(\frac{1}{2}\) and \(BC = 8\)): \[ \frac{1}{2} = \frac{8}{EF} \] 4. Cross-multiply to solve for \(EF\): \[ EF = 8 \times 2 = 16 \text{ cm} \]
Step 4: Final Answer:
The length of \(EF\) is 16 cm.