Question

If \(\triangle ABC \sim \triangle DEF\) such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then the perimeter of \(\triangle ABC\) is :

• A. 7.5 cm
• B. 15 cm
• C. 11.5 cm
• D. 9.5 cm

Hint:

Notice that side \(BC\) is exactly twice the corresponding side \(EF\) (\(4\text{ cm} = 2 \times 2\text{ cm}\)).
This means the scale factor of similarity is \(2\).
Therefore, the perimeter of \(\triangle ABC\) must be exactly twice the perimeter of \(\triangle DEF\):
\[ 2 \times (3 + 2 + 2.5) = 2 \times 7.5 = 15\text{ cm} \]

Answer 1

The Correct Option is B

Step 1: Find the scale factor between the two triangles.
Since $\triangle ABC \sim \triangle DEF$, side $BC$ corresponds to side $EF$. \[ k = \frac{BC}{EF} = \frac{4}{2} = 2 \]
Step 2: Scale up every side of DEF individually. \[ AB = k \times DE = 2 \times 3 = 6 \text{ cm} \] \[ AC = k \times DF = 2 \times 2.5 = 5 \text{ cm} \] and we already know $BC = 4$ cm.
Step 3: Add the three sides of triangle ABC. \[ \text{Perimeter} = AB + BC + AC = 6 + 4 + 5 = 15 \text{ cm} \]
Step 4: Conclude. \[ \boxed{15 \text{ cm}} \]