Two similar triangles have areas 81 cm² and 144 cm². If the largest side of the smaller triangle is 27 cm, find the largest side of the larger triangle.

Introduction / Context:
For similar triangles, the ratio of areas equals the square of the ratio of corresponding side lengths. We can extract the linear scale factor by taking square roots of the area ratio.

Given Data / Assumptions:

• Areas: 81 and 144 cm² (smaller to larger).
• Largest side (smaller) = 27 cm.

Concept / Approach:
If k is the linear scale (larger/smaller), then area ratio = k². Hence k = √(144/81). Multiply the smaller corresponding side by k to get the larger side.

Step-by-Step Solution:

Verification / Alternative check:
(36/27)² = (4/3)² = 16/9; 81 * (16/9) = 144 ✓.

Why Other Options Are Wrong:
48 cm uses a scale of 16/9 on length; 24 cm uses 8/9; 88 cm is unrelated to the scale ratio.

Common Pitfalls:
Using area ratio directly on sides without taking the square root first.

Final Answer:
36 cm