Question

(a) one triangle has side lengths 14, 11, and 12. compute the sum of the squares of the shorter lengths. $11^2 + 12^2 = \square$ compute the square of the longest length. $14^2 = \square$ what kind of triangle is it? $\circ$ acute triangle $\circ$ right triangle $\circ$ obtuse triangle (b) the other triangle has side lengths 18, 14, and 6. compute the sum of the squares of the shorter lengths. $6^2 + 14^2 = \square$ compute the square of the longest length. $18^2 = \square$ what kind of triangle is it? $\circ$ acute triangle $\circ$ right triangle $\circ$ obtuse triangle

Explanation:

Step1: Calcular \(11^2 + 12^2\)

\(11^2 = 121\), \(12^2 = 144\), entonces \(11^2 + 12^2 = 121 + 144 = 265\).

Step2: Calcular \(14^2\)

\(14^2 = 196\).

Step3: Comparar y determinar el triángulo (a)

Como \(11^2 + 12^2 = 265\) y \(14^2 = 196\), y \(265>196\) (es decir, \(a^2 + b^2>c^2\) donde \(c\) es el lado más largo), el triángulo es acutángulo.

Step4: Calcular \(6^2 + 14^2\)

\(6^2 = 36\), \(14^2 = 196\), entonces \(6^2 + 14^2 = 36 + 196 = 232\).

Step5: Calcular \(18^2\)

\(18^2 = 324\).

Step6: Comparar y determinar el triángulo (b)

Como \(6^2 + 14^2 = 232\) y \(18^2 = 324\), y \(232<324\) (es decir, \(a^2 + b^2

Answer:

(a) \(11^2 + 12^2 = 265\), \(14^2 = 196\), Triángulo: Acute triangle
(b) \(6^2 + 14^2 = 232\), \(18^2 = 324\), Triángulo: Obtuse triangle