Question

The base of two similar triangles are 24 cm and 18 cm. If one side of the first triangle is 8 cm then corresponding side of other triangle is

• A. 8 cm
• B. 6 cm
• C. 4 cm
• D. 2 cm

Answer 1

The Correct Option is B

To solve the problem, we need to determine the corresponding side of the second triangle given that the two triangles are similar. Let us analyze this step by step.

1. Understanding Similar Triangles:
When two triangles are similar, their corresponding sides are proportional. This means the ratio of the lengths of corresponding sides is constant.

2. Given Information:
The bases of the two similar triangles are \( 24 \, \text{cm} \) and \( 18 \, \text{cm} \). One side of the first triangle is \( 8 \, \text{cm} \), and we need to find the corresponding side of the second triangle.

3. Ratio of Corresponding Sides:
The ratio of the bases of the two triangles gives the scale factor between the two triangles:

$$ \text{Ratio} = \frac{\text{Base of First Triangle}}{\text{Base of Second Triangle}} = \frac{24}{18} = \frac{4}{3} $$

This ratio applies to all corresponding sides of the triangles. Therefore, if one side of the first triangle is \( 8 \, \text{cm} \), the corresponding side of the second triangle can be found using the same ratio:

$$ \text{Corresponding Side of Second Triangle} = \frac{\text{Side of First Triangle}}{\text{Ratio}} = \frac{8}{\frac{4}{3}} = 8 \times \frac{3}{4} = 6 \, \text{cm} $$

4. Conclusion:
The corresponding side of the second triangle is \( 6 \, \text{cm} \).

Final Answer:
The correct option is \( {6 \, \text{cm}} \).