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

Given that \(\Delta ABC\) and \(\Delta DEF\) are similar triangles. By the property of similar triangles, corresponding sides are in proportion. Therefore, we have:

\(\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}\)

We are also given the condition \(2 AB = DE\). So, substituting this into the ratio, we get:

\(\frac{AB}{2AB} = \frac{BC}{EF}\)

Simplifying the left side of the equation:

\(\frac{1}{2} = \frac{BC}{EF}\)

We are provided with \(BC = 8\) cm. Substituting \(BC\) into the equation gives:

\(\frac{1}{2} = \frac{8}{EF}\)

To find the value of \(EF\), cross-multiply to solve for \(EF\):

\(EF \cdot 1 = 8 \times 2\)

Simplifying the right side, we have:

\(EF = 16\) cm

Hence, the length of \(EF\) is 16 cm.

The correct answer is therefore 16 cm. This follows from the properties of similar triangles and utilizing the given conditions effectively.