Two similar triangles have areas in the ratio 9:25. If the shorter side of the smaller triangle is 6 cm, what is the corresponding side in the larger triangle?

Thu, 30 Apr 2026 09:30:29 +0000

**Two similar triangles have areas in the ratio 9:25. If the shorter side of the smaller triangle is 6 cm, what is the corresponding side in the larger triangle?** In today’s world of visual learners and mobile-first exploration, a quiet mathematical insight keeps resurfacing in home improvement forums, design apps, and education groups: when two similar triangles share proportional sides, their areas follow a predictable pattern—specifically, a ratio based on the square of their side-length ratio. This principle explains why beginners and enthusiasts alike focus closely on triangle geometry when solving proportional puzzles. With many newcomers exploring the topic for home projects, learning materials, or creative problem-solving, understanding how this area ratio works reveals both mathematical consistency and practical value. ### Why This Ratio Matters Now The idea that area scales with the square of side proportions is more than a textbook rule—it’s actively discussed across platforms where spatial reasoning matters. With growing interest in architecture, interior design, 3D modeling, and even cryptography-based puzzles, recognizing how ratios translate across shapes helps users grasp foundational geometry principles. The 9:25 ratio signals that the larger triangle’s linear dimensions are 5 times those of the smaller—proven by squaring the square root of 25 divided by 9, resulting in the scale factor 5 (since √25 = 5). This proportional growth confirms that geometry remains a core skill in modern visual literacy and design thinking.