Question

If the ratio of areas of two similar triangles is 100 : 144 then the ratio of their corresponding sides is

• A. 10 : 8
• B. 12 : 10
• C. 10 : 12
• D. 10 : 13

Hint:

Remember the relationship: Ratio of Sides = \(r\), Ratio of Areas = \(r^2\), Ratio of Volumes (for similar solids) = \(r^3\). To go from area to side, you need to take the square root.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
There is a fundamental theorem in geometry that relates the areas of similar triangles to their corresponding sides.

Step 2: Key Formula or Approach:
If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
\[ \frac{\text{Area}_1}{\text{Area}_2} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2 \] Therefore, the ratio of the sides is the square root of the ratio of the areas.
\[ \frac{\text{Side}_1}{\text{Side}_2} = \sqrt{\frac{\text{Area}_1}{\text{Area}_2}} \]

Step 3: Detailed Explanation:
We are given the ratio of the areas:
\[ \frac{\text{Area}_1}{\text{Area}_2} = \frac{100}{144} \] To find the ratio of the corresponding sides, we take the square root:
\[ \frac{\text{Side}_1}{\text{Side}_2} = \sqrt{\frac{100}{144}} = \frac{\sqrt{100}}{\sqrt{144}} = \frac{10}{12} \] So, the ratio of the corresponding sides is 10 : 12.

Step 4: Final Answer:
The ratio of their corresponding sides is 10 : 12.