Question

determine whether a triangle with the given side lengths is a right triangle.
side lengths right triangle not a right triangle not enough information
(a) 6, 9, 11
(b) 13, 20, 26
(c) 20, 21, 29
(d) 5, 11, 12

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check (a) 6, 9, 11

Calculate \(6^{2}+9^{2}=36 + 81=117\) and \(11^{2}=121\). Since \(117
eq121\), it is not a right - triangle.

Step3: Check (b) 13, 20, 26

Calculate \(13^{2}+20^{2}=169+400 = 569\) and \(26^{2}=676\). Since \(569
eq676\), it is not a right - triangle.

Step4: Check (c) 20, 21, 29

Calculate \(20^{2}+21^{2}=400 + 441=841\) and \(29^{2}=841\). Since \(20^{2}+21^{2}=29^{2}\), it is a right - triangle.

Step5: Check (d) 5, 11, 12

Calculate \(5^{2}+11^{2}=25+121 = 146\) and \(12^{2}=144\). Since \(146
eq144\), it is not a right - triangle.

Answer:

(a) Not a right triangle
(b) Not a right triangle
(c) Right triangle
(d) Not a right triangle