Question

multiple choice 1 point
can a triangle have sides with the given lengths? explain.
a = 3 yd, b = 7 yd, c = 8 yd
no because the sum of the lengths of the two shorter sides is greater than the length of the
third side, and this contradicts the triangle inequality theorem.
yes because the sum of the lengths of any two sides is greater than the length of the third
side.
yes because the sum of the lengths of the two shorter sides is less than the length of the third
side and this satisfies the triangle inequality theorem.
no because the sum of the lengths of the two shorter sides and this contradicts the triangle inequality theorem.

Explanation:

Step1: Aplicar la desigualdad triangular

La desigualdad triangular establece que la suma de las longitudes de cualquier par de lados de un triángulo debe ser mayor que la longitud del tercer lado.

Step2: Verificar las desigualdades

1. \(a + b>c\): \(3 + 7>8\) → \(10>8\) (verdadero)
2. \(a + c>b\): \(3+8>7\) → \(11>7\) (verdadero)
3. \(b + c>a\): \(7 + 8>3\) → \(15>3\) (verdadero)

Answer:

Yes because the sum of the lengths of any two sides is greater than the length of the third side.