Question

\(\triangle ABC \sim \triangle DEF\) and their areas are respectively \(81 \text{ cm}^2 \quad \text{and} \quad 225 \text{ cm}^2\); if \(EF = 5 cm\), then \(BC=\)

• A. 3 cm
• B. 9 cm
• C. 10 cm
• D. 5 cm

Answer 1

The Correct Option is A

To solve the problem, we need to find the length of side $BC$ in triangle $ABC$ using the fact that $\triangle ABC \sim \triangle DEF$.

1. Understanding Similar Triangles:

When two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

$ \frac{\text{Area}_{ABC}}{\text{Area}_{DEF}} = \left( \frac{BC}{EF} \right)^2 $

2. Substituting Known Values:

Given:

Area of $\triangle ABC = 81 \, \text{cm}^2$

Area of $\triangle DEF = 225 \, \text{cm}^2$

$EF = 5 \, \text{cm}$

So,

$ \frac{81}{225} = \left( \frac{BC}{5} \right)^2 $

3. Simplifying the Ratio:

$ \left( \frac{BC}{5} \right)^2 = \frac{81}{225} = \frac{9^2}{15^2} $

Taking square roots on both sides:

$ \frac{BC}{5} = \frac{9}{15} = \frac{3}{5} $

4. Solving for $BC$:

$BC = 5 \times \frac{3}{5} = 3 \, \text{cm}$

Final Answer: $BC = 3 \, \text{cm}$