A triangle has sides in the ratio 5:12:13. If the shortest side is 10 cm, what is the area of the triangle? - NBX Soluciones
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:
📰 live now before livystore runs out—exclusive drops you won’t believe 📰 livystore holds the magic—what secrets are hiding in your cart? 📰 don’t let livystore disappear forever—your favorite finds are slipping away 📰 Shocking Gold Hoop Earrings Thatll Make You The Center Of Every Party 8876554 📰 Black Led Lights That Shine Bright Without Blinkingperfect For Every Cool Ambient Setup 824143 📰 Didgeridoo Mastery These Rare Instruments Prove Its Traditional Magic Still Thrives 3888740 📰 Go Viral Brenda Songs Scandalous Nude Moment Leaves The World Speechless 9988793 📰 Tampa To New York Flights 7743453 📰 Can These Coffin Shaped Nails Make You The Most Instagrammable Person Find Out 2469617 📰 Dont Miss These Shocking Mp Reviewstheyll Rewrite Your Purchase Decision 6986279 📰 Service Integration Bus The Game Changer Proven To Slash Integration Costs Boost Speed 8286907 📰 Roblox Gift Ards 4324538 📰 Screenshot On Laptop 5493600 📰 50 States Map Quiz 3564626 📰 You Wont Believe What Happened At Itsrandalinthis Moment Stunned Everyone 6705405 📰 Arctic Monkeys Do U Wanna Know Lyrics 5429567 📰 Jim White Toyota 8684708 📰 Why Greenport Is Hidden Under Nycs Radaryou Wont Believe Whats Growing Beneath The Streets 711709Final 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!
