Which of the following is a Pythagorean triplet?

Question

Examoogle · Accepted Answer

The correct answer is Option B: $(8, 15, 17)$. Check the condition a^2 + b^2 = c^2 for the largest number c in each set. For (8, 15, 17), 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289. Since 289 = 289, it is a Pythagorean triplet.

Step-by-Step Solution & Concepts:
Shortcut Trick: Check the condition a^2 + b^2 = c^2 for the largest number c in each set. For (8, 15, 17), 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289. Since 289 = 289, it is a Pythagorean triplet.

Formula Used: $$a^2 + b^2 = c^2$$

Given: A set of three numbers (a, b, c) is a Pythagorean triplet if it satisfies the Pythagorean theorem: a^2 + b^2 = c^2, where c is the largest number.

Steps: Define Pythagorean Triplet: A set of three positive integers $(a, b, c)$ is called a Pythagorean triplet if they satisfy the equation of a right-angled triangle.. Evaluate Option A: (6, 9, 11): Calculating squares: $6^2 + 9^2 = 36 + 81 = 117$. Comparing to $11^2 = 121$. Since $117 
eq 121$, it is not a triplet.. Evaluate Option B: (8, 15, 17): Calculating squares: $8^2 + 15^2 = 64 + 225 = 289$. Comparing to $17^2 = 289$. Since $289 = 289$, it is a valid Pythagorean triplet.. Verify remaining options: Option C $(2, 3, 5): 4 + 9 = 13 
eq 25$. Option D $(5, 7, 9): 25 + 49 = 74 
eq 81$. Neither are valid.

Answer: B is correct because the set (8, 15, 17) satisfies the Pythagorean theorem $8^2 + 15^2 = 17^2$.

Exam Tip: This concept is fundamental to trigonometry and coordinate geometry, specifically when finding the distance between two points on a Cartesian plane.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)