Question

determine whether a triangle with the given side lengths is a right triangle.
side lengths\tright triangle\tnot a right triangle\tnot enough information
(a) 5, 12, 13\t○\t○\t○
(b) 14, 48, 50\t○\t○\t○
(c) 8, 11, 14\t○\t○\t○
(d) 10, 26, 28\t○\t○\t○

Explanation:

Step1: Check (a) 5,12,13 with Pythagoras

$5^2 + 12^2 = 25 + 144 = 169 = 13^2$ → Right triangle

Step2: Check (b)14,48,50 with Pythagoras

$14^2 + 48^2 = 196 + 2304 = 2500 = 50^2$ → Right triangle

Step3: Check (c)8,11,14 with Pythagoras

$8^2 + 11^2 = 64 + 121 = 185 ≠ 14^2=196$ → Not a right triangle

Step4: Check (d)10,26,28 with Pythagoras

$10^2 + 26^2 = 100 + 676 = 776 ≠ 28^2=784$ → Not a right triangle

Answer:

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