A triangle has sides in the ratio 5:12:13. If the shortest side is 10 cm, what is the area of the triangle? - Midis
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:
📰 Borderland Beat That’s Making Hearts Race and Fingertips Tingle 📰 Borderland Beat Unleashed—This Hidden Sound is Taking Over Towns! 📰 Boston Baked Beans Hidden Love in Every Jar – You Won’t Believe What’s Inside! 📰 What Is The Beyonder The Untold Truth Behind This Hidden Power 📰 What Is The Darkness Game This Hidden Phenomenon Will Change Everything You Know 📰 What Lies Behind The Tears Of The Kingdom The Game Critical Reveal You Needed 📰 What Lies Beyond Reality The Twilight Zone Movie Youve Been Matched With 📰 What Lies Beyond The Thousand Year Door Ancient Mysteries You Wont Believe 📰 What Lies Within The Mystery Spot Insane Facts That Will Blow Your Mind 📰 What Made The 1990 Flash Tv Series Unforgettable Dont Miss These Shocking Facts 📰 What Makes Team 7 Naruto A Legend Shocking Insights You Wont Believe 📰 What Makes Teres Major Steak The Hottest Trend Expert Breakdown Insideyoull Love It 📰 What Makes The Boys Characters So Unforgettable A Deep Dive Into Their Cold Calculated Minds 📰 What Makes The Leader Marvel Unstoppable Discover The Mind Blowing Truth 📰 What Makes The Ruler Game So Unbeatable The Surprising Secrets You Wont Want To Miss 📰 What No Ones Talking About Shocking Details Behind This Hottest Tv Series Scandal Yet 📰 What Secret Alliance In Tales Of Arise Will Change Your Perspective Forever 📰 What Secret Did Bones Reveal About Its Final Season Quiz Results Will Shock YouFinal 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!
