Question

determine whether a triangle with the given side lengths is a right triangle.
side lengths\t(a) 8, 15, 17\t(b) 4, 7, 8\t(c) 22, 29, 36\t(d) 10, 24, 26
right triangle\t○\t○\t○\t○
not a right triangle\t○\t○\t○\t○
not enough information\t○\t○\t○\t○

Explanation:

Step1: Analizar (a) 8, 15, 17

Comprobar el teorema de Pitágoras: \(8^2 + 15^2 = 64 + 225 = 289\) y \(17^2 = 289\). Entonces \(8^2 + 15^2 = 17^2\), es triángulo rectángulo.

Step2: Analizar (b) 4, 7, 8

\(4^2 + 7^2 = 16 + 49 = 65\) y \(8^2 = 64\). \(65
eq64\), no es triángulo rectángulo.

Step3: Analizar (c) 22, 29, 36

\(22^2 + 29^2 = 484 + 841 = 1325\) y \(36^2 = 1296\). \(1325
eq1296\), no es triángulo rectángulo.

Step4: Analizar (d) 10, 24, 26

\(10^2 + 24^2 = 100 + 576 = 676\) y \(26^2 = 676\). Entonces \(10^2 + 24^2 = 26^2\), es triángulo rectángulo.

Answer:

(a) 8, 15, 17: Right triangle
(b) 4, 7, 8: Not a right triangle
(c) 22, 29, 36: Not a right triangle
(d) 10, 24, 26: Right triangle