Question

students measure the sides of 4 triangles in a test. the lengths of the sides of the different triangles follow: triangle 1: 6, 12 and 13 triangle 2: 5, 12 and 13 triangle 3: 3, 4 and 5 triangle 4: 2, 4 and 6 using the pythagorean theorem, which of the triangles are right triangles? select all that apply. triangle 4 triangle 1 triangle 2 triangle 3

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check Triangle 1

\(a = 6\), \(b = 12\), \(c = 13\). Calculate \(a^{2}+b^{2}=6^{2}+12^{2}=36 + 144=180\), and \(c^{2}=13^{2}=169\). Since \(180
eq169\), Triangle 1 is not a right - triangle.

Step3: Check Triangle 2

\(a = 5\), \(b = 12\), \(c = 13\). Calculate \(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144 = 169\), and \(c^{2}=13^{2}=169\). Since \(a^{2}+b^{2}=c^{2}\), Triangle 2 is a right - triangle.

Step4: Check Triangle 3

\(a = 3\), \(b = 4\), \(c = 5\). Calculate \(a^{2}+b^{2}=3^{2}+4^{2}=9 + 16=25\), and \(c^{2}=5^{2}=25\). Since \(a^{2}+b^{2}=c^{2}\), Triangle 3 is a right - triangle.

Step5: Check Triangle 4

\(a = 2\), \(b = 4\), \(c = 6\). Calculate \(a^{2}+b^{2}=2^{2}+4^{2}=4 + 16 = 20\), and \(c^{2}=6^{2}=36\). Since \(20
eq36\), Triangle 4 is not a right - triangle.

Answer:

Triangle 2, Triangle 3