Question

Areas of two similar triangles are in the ratio $16 : 25$. The ratio of corresponding sides of the triangles will be:

• A. $5 : 4$
• B. $4 : 5$
• C. $3 : 5$
• D. $16 : 9$

Hint:

For similar figures, the ratio of areas is the square of the ratio of corresponding sides.

Answer 1

The Correct Option is B

Step 1: Recall the relationship between areas and corresponding sides of similar triangles.
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. \[ \frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \left(\frac{\text{Side of Triangle 1}}{\text{Side of Triangle 2}}\right)^2 \]
Step 2: Use the given area ratio.
We are given that the areas of the two triangles are in the ratio $16 : 25$. Thus, \[ \frac{16}{25} = \left(\frac{\text{Side 1}}{\text{Side 2}}\right)^2 \]
Step 3: Take the square root of both sides.
\[ \frac{\text{Side 1}}{\text{Side 2}} = \sqrt{\frac{16}{25}} = \frac{4}{5} \]
Step 4: Conclusion.
The ratio of the corresponding sides of the two triangles is $4 : 5$.