Question

determine whether a triangle with the given side lengths is a right triangle. (a) 4, 8, 9 (b) 20, 21, 29 (c) 11, 13, 17 (d) 3, 9, 10

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) 4, 8, 9

\(4^{2}+8^{2}=16 + 64=80\), and \(9^{2}=81\). Since \(80
eq81\), it's not a right - triangle.

Step3: Check (b) 20, 21, 29

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

Step4: Check (c) 11, 13, 17

\(11^{2}+13^{2}=121 + 169=290\), and \(17^{2}=289\). Since \(290
eq289\), it's not a right - triangle.

Step5: Check (d) 3, 9, 10

\(3^{2}+9^{2}=9 + 81=90\), and \(10^{2}=100\). Since \(90
eq100\), it's not a right - triangle.

Answer:

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