Question

38 the sides of triangle abc measure 10, 12, and 15 centimeters. the sides of triangle def measure 12, 16, and 20 inches. which statement about the triangles is true? a triangle def is a right triangle; triangle abc is not a right triangle. b triangle abc is a right triangle; triangle def is not a right triangle. c triangle abc and triangle def are both right triangles. d neither triangle abc nor triangle def is a right triangle.

Explanation:

Step1: Verificar Triángulo ABC (10, 12, 15)

Para un triángulo rectángulo, debe cumplirse el Teorema de Pitágoras: \(a^2 + b^2 = c^2\) (donde \(c\) es el lado más largo).
Calculamos: \(10^2 + 12^2 = 100 + 144 = 244\) y \(15^2 = 225\).
Como \(244
eq 225\), ABC no es rectángulo.

Step2: Verificar Triángulo DEF (12, 16, 20)

Aplicamos el Teorema de Pitágoras: \(12^2 + 16^2 = 144 + 256 = 400\) y \(20^2 = 400\).
Como \(12^2 + 16^2 = 20^2\), DEF es rectángulo.

Answer:

A. Triangle DEF is a right triangle; triangle ABC is not a right triangle.