A triangle has side lengths of 1, 1 - c, and 1 - 2c. What are all the possible values of c?

Guest May 14, 2020

#1**0 **

So a triangle's legs' sum must exceed the hypothenuse to be a triangle.

First, assuming c is positive, we have 1-2c and 1-c as the legs as they are each smaller than 1.

So,.

1-2c + 1-c >1

2-3c >1

1 >3c

1/3 >c

c < 1/3

That's after a bit of rearrangement.

NOW assuming c is 0. Hmm. That doesn't work since 1+1 = 2. Hmm.

NOW assuming that c is negative.

1-2c must be the hypothenuse as it is the largest, and 1 and 1-c are the legs.

1 + 1-c > 1-2c

2-c > 1-2c

1 > 2c

1/2 > c

c < 1/2

since c is smaller than 1/2 AND 1/3, we go with 1/3 since it's smaller than and the smallest.

c <1/3

If you don't understand anythign feel free to ask.

hugomimihu May 14, 2020