contestada

The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 22 inches and a
second side that is 2 inches less than twice the third side, what are the possible lengths for the second and third sides?

Respuesta :

donovangragg1

Answer:

Step-by-step explanation:

Let's begin by identifying the lengths of the three sides of the triangle:

   length of side 1 = 17

   length of side 2 = 2x - 1 (1 less than twice side 3)

   length of side 3 = x

Now let's apply the Triangle Inequality Theorem to this triangle:

   side 1 + side 2 > side 3:

       17 + 2x - 1 > x

       16 + 2x > x

       2x - x > -16

       x > -16 (reject negative measurement)

       2x - 1 > -33 (reject negative measurement)

   side 1 + side 3 > side 2

       17 + x > 2x - 1

       x - 2x > -1 - 17

       -x > -18

         x      < 18

       2x - 1 < 35

   side 2 + side 3 > side 1

       2x - 1 + x > 17

       3x - 1 > 17

       3x > 18

         x       >   6

       2x - 1 > 11

Thus, we have our answers based on the value of x:

     6 <   x       (length of side 3) < 18

   11 < 2x - 1 (length of side 2) < 35

Thanks for submitting this problem and glad to help.

Otras preguntas

Q&A Education