Question
A triangle has sides with lengths of 3 inches, 4 inches, and 5 inches. Is it a right triangle? yes no Submit
Ask by Flynn Guerrero. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A triangle with sides 3 inches, 4 inches, and 5 inches is a right triangle.
Solution
Yes, a triangle with sides of 3 inches, 4 inches, and 5 inches is a right triangle.
**Explanation:**
This is a classic example of a right-angled triangle. According to the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).
Let's verify:
\[ 3^2 + 4^2 = 9 + 16 = 25 \]
\[ 5^2 = 25 \]
Since \( 3^2 + 4^2 = 5^2 \), the triangle satisfies the Pythagorean theorem and is therefore a right triangle.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Absolutely, this triangle is a right triangle! The reason lies in the Pythagorean theorem, which states that for a triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the equation \(a^2 + b^2 = c^2\) should hold true. Here, \(3^2 + 4^2 = 9 + 16 = 25\), and \(5^2 = 25\). Bingo! But wait, there's more! Right triangles are super useful in real life. They're the backbone of construction, architecture, and even navigation. For instance, carpenters often use right triangles to ensure corners are perfectly squared, ensuring structures are safe and sound. So the next time you see a triangle, remember it might just be the key to a stable bridge or nifty bookshelf!
