the sum of the lengths of any 2 sides of a triangle must be greater than the third side. one side is 17cm and second side is 1 cm less than twice the third side

Question

the sum of the lengths of any 2 sides of a triangle must be greater than the third side. one side is 17cm and second side is 1 cm less than twice the third side. what are the possible lengths for the second and third sides?

Answer 1

Hi Hannah,

 

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.

 

God bless, Jordan.