A triangle has sides in the ratio 5:12:13. If the shortest side is 10 cm, what is the area of the triangle? - Sterling Industries
Using the 5:12:13 Triangle Ratio to Find Area – A Simple Geometry Guide
Using the 5:12:13 Triangle Ratio to Find Area – A Simple Geometry Guide
A triangle with sides in the ratio 5:12:13 is a classic example of a right triangle. If the shortest side measures 10 cm and follows this ratio, it serves as a perfect starting point to explore triangle properties—especially area calculation.
In a 5:12:13 triangle, the sides are proportional to 5k, 12k, and 13k, where k is a scaling factor. Since the shortest side is 10 cm and corresponds to 5k, we solve:
Understanding the Context
\[
5k = 10 \implies k = 2
\]
Using this factor:
- Second side = 12k = 12 × 2 = 24 cm
- Longest side = 13k = 13 × 2 = 26 cm
Because 5² + 12² = 25 + 144 = 169 = 13², this triangle is a right triangle, with the right angle between the sides of 10 cm and 24 cm.
Image Gallery
Key Insights
Calculating the Area
For a right triangle, area is simply:
\[
\ ext{Area} = \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}
\]
Here, base = 10 cm and height = 24 cm:
\[
\ ext{Area} = \frac{1}{2} \ imes 10 \ imes 24 = \frac{1}{2} \ imes 240 = 120~\ ext{cm}^2
\]
🔗 Related Articles You Might Like:
📰 Gatecrashers Alert: American Eagle Outfitters Trading Explosion, Yahoo Finance Confirms! 📰 Breakout Alert: AMGN Stock Skyrockets 200%—You Need to Act Now Before It Shuts Down! 📰 AMGN Stock Mystery Unveiled: Is This the Next Revolutionary Wave? Dont Miss Out! 📰 How To Delete How To Delete 📰 Roblox Accesories 📰 You Didnt Realize Thanksgiving Memes Were This Destroyingheres The Ultimate Humor Twist 6927172 📰 Mount And Blade Fire And Sword 📰 Fast And Furious Seven Cars 📰 Bug Bite Identifier App 📰 Best Stocks 2025 📰 2 Cash Back Credit Cards 📰 Is This The Mysterious Unicorn Iverlord Weve All Been Waiting For Watch Now 7789083 📰 Text Editor For Mac 📰 Solution Recognize It As A Difference Of Cubes 2A3 3B3 8A3 27B3 Alternatively Expand Directly 2431086 📰 Create Your Own Game On Roblox 📰 Roblox Photos 📰 Tesla Stock Price Prediction 2025 8194258 📰 Wordle 1605 AnswerFinal Thoughts
So, the area of the triangle with sides in the ratio 5:12:13 and shortest side 10 cm is 120 square centimeters.
Why This Ratio Matters
The 5:12:13 triangle is famous because it generates one of the smallest whole-number-sided Pythagorean triples. This makes it ideal for geometry lessons, construction, and understanding proportional relationships in right triangles.
If you’re studying triangles, recognizing this ratio helps simplify calculations—especially area and perimeter—without complex formulas.
In summary:
- Ratio: 5:12:13
- Shortest side: 10 cm → k = 2
- Other sides: 24 cm and 26 cm
- Area: 120 cm²
Mastering these basic triangles builds a strong foundation in geometry!
