Question**: A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? - Decision Point
Is a Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle? A Clear Geometry Check
Is a Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle? A Clear Geometry Check
When studying triangles, one common question students face is whether a three-sided figure with given side lengths — such as 7 cm, 24 cm, and 25 cm — is a right triangle. In this article, we’ll clearly explain how to determine if this triangle satisfies the key condition of being a right triangle and verify its classification using the Pythagorean theorem.
What is a Right Triangle?
Understanding the Context
A right triangle is defined as a triangle that contains one angle measuring exactly 90 degrees. The side opposite this right angle is called the hypotenuse, the longest side of the triangle. For a triangle with sides a, b, and c (where c is the longest side), it is a right triangle if:
\[
a^2 + b^2 = c^2
\]
This is the well-known Pythagorean Theorem.
Image Gallery
Key Insights
Analyzing the Given Triangle
We are given side lengths: 7 cm, 24 cm, and 25 cm.
First, identify the longest side:
- 7 cm < 24 cm < 25 cm ⇒ The longest side is 25 cm, which we assume could be the hypotenuse.
Now, apply the Pythagorean theorem to test:
\[
7^2 + 24^2 = ?
\]
\[
49 + 576 = 625
\]
🔗 Related Articles You Might Like:
📰 Finding Your Perfect Fit: Snowboard Size Chart You Were Built to Love! 📰 Shop Smarter: The Hot Snowboard Size Chart Everyone Searches For Online! 📰 Snow White Movie Review: Is Disney’s Classic Still Timeless in 2024? You Won’t Believe For You! 📰 Hawkgirl Real Name 8883015 📰 You Wont Believe What Happens When Basketball Startssee Why Fans Wont Stop Talking 1923012 📰 The Real Mimi R34S Hidden Move Proves Shes Unstoppable Forever 3614498 📰 Spa Francorchamps 3888542 📰 Emx Royalty Stock 7049863 📰 Bob Gosse 9832268 📰 Step Into Ohios Future With Fidelity Polaris How This Innovator Shocks The Market 2537905 📰 Civilization 4 1747436 📰 A Lot Of Games 4863544 📰 Texan Slang 6704771 📰 Chatit Secrets Revealed How This App Outshines Every Other Chat Platform 8644312 📰 My Life With The Walter Boys Season 1 5808483 📰 Whats Hiding In The Nudogram Mind Blowing Truths Unveiled 9145168 📰 Book People Uncover The Surprising Reasons Behind Their Reading Fix 133749 📰 30 Second Note Thatll Change How You Organize Your Day Forever 3800899Final Thoughts
\[
25^2 = 625
\]
Since both expressions are equal:
\[
7^2 + 24^2 = 25^2
\]
This confirms the triangle satisfies the Pythagorean Theorem.
Conclusion: Yes, It Is a Right Triangle
Because the squares of the two shorter sides (7 cm and 24 cm) add up exactly to the square of the longest side (25 cm), this triangle is a right triangle. It has a right angle opposite the 25 cm side, making it a classic example of a 7-24-25 right triangle — one of the well-known Pythagorean triples.
Why This Matters
Understanding whether triangles like this are right-angled is fundamental in geometry, trigonometry, architecture, engineering, and math education. Recognizing right triangles helps in calculating area, verifying structural stability, and solving real-world problems involving angles and distances.
