Two similar triangles have areas 121 cm² and 81 cm². Find the ratio of their corresponding heights (altitudes).

Introduction / Context:In similar triangles, all corresponding linear dimensions (sides, medians, altitudes) are in the same ratio, which is the square root of the area ratio.

Given Data / Assumptions:

• Areas: 121 and 81 cm².
• Triangles are similar.

Concept / Approach:If linear scale factor is k, then area scale factor is k². Hence k = √(area ratio). The ratio of corresponding heights equals k.

Step-by-Step Solution:Area ratio = 121 : 81 = 11² : 9².So linear ratio (including altitudes) = 11 : 9.

Verification / Alternative check:Any pair of corresponding sides would also be in 11:9, confirming consistency.

Why Other Options Are Wrong:22:9 and 33:6 do not reflect square roots; 11:18 inverts one factor.

Common Pitfalls:Using the area ratio directly as the side/altitude ratio instead of its square root.

Final Answer:11 9