Question

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

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

Hint:

The relation $2 \text{ AB} = \text{DE}$ tells us that each side of the second triangle ($\Delta \text{DEF}$) is exactly twice the length of the corresponding side of the first triangle ($\Delta \text{ABC}$).
Since $\text{BC} = 8 \text{ cm}$, EF must be $2 \times 8 = 16 \text{ cm}$.

Answer 1

The Correct Option is D

Step 1: Read the scale factor straight from the given relation.
We're told $2\,\text{AB}=\text{DE}$, which simply means every side of $\Delta$DEF is exactly twice the matching side of $\Delta$ABC.
Step 2: Apply that same doubling to side BC.
Since $\Delta$ABC $\sim$ $\Delta$DEF, side EF corresponds to side BC, so EF must also be double BC.
Step 3: Compute the length.
$\text{EF} = 2 \times \text{BC} = 2 \times 8 = 16$ cm.
\[ \boxed{16 \text{ cm}} \]