Question

question 9. side lengths right triangle not a right triangle 2, 3, 5 3, 4, 5 6, 8, 12 7, 24, 25 15, 20, 25

Explanation:

Step1: Apply Pythagorean theorem

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), check if \(a^{2}+b^{2}=c^{2}\)

For \(2\), \(3\), \(5\)

\(2^{2}+3^{2}=4 + 9=13\), \(5^{2}=25\), \(13
eq25\)

For \(3\), \(4\), \(5\)

\(3^{2}+4^{2}=9+16 = 25\), \(5^{2}=25\), \(25 = 25\)

For \(6\), \(8\), \(12\)

\(6^{2}+8^{2}=36 + 64=100\), \(12^{2}=144\), \(100
eq144\)

For \(7\), \(24\), \(25\)

\(7^{2}+24^{2}=49+576 = 625\), \(25^{2}=625\), \(625=625\)

For \(15\), \(20\), \(25\)

\(15^{2}+20^{2}=225+400 = 625\), \(25^{2}=625\), \(625=625\)

Answer:

• \(2\), \(3\), \(5\): Not a Right Triangle
• \(3\), \(4\), \(5\): Right Triangle
• \(6\), \(8\), \(12\): Not a Right Triangle
• \(7\), \(24\), \(25\): Right Triangle
• \(15\), \(20\), \(25\): Right Triangle