Geometry Triangle Question?

Question

Question: The measures of two sides of a triangle are 21 and 27. Which number COULD NOT be the third side of the triangle? (note it doesn't say the two given measurements are legs)

Answer 1

In order for 3 lengths to creat a triangle, the sum of the two smaller lengths must be GREATER than the larger. If it's less than or even equal to the third side, it does not create a triangle. Since you were only given 2 lengths you need to find the possibilites of x by setting up the following 3 inequalities:

a. 21 + 27 > x
b. x + 21 > 27
c. x + 27 > 21

Now, solve each of these inequalities for x.

a. 48 > x
b. x > 6
c. x > -6 < ---- Note, this solution makes no sense since lengths of sides cannot be negative.

From these three solutions we can determine that x must be between 6 and 48 ( 6 < x < 48 ). Therefore, any number that is NOT between 6 and 48 is not a possible answer for the third side. (note is also cannot include 6 and 48 - it must be greater than 6 or less than 48)

Answer 2

The sum of any two sides of a triangle must be greater than the third side. You can see this for yourself if you take two even strips of paper, tear one of them into two pieces, then try to make a triangle out of them; you can't because at least one piece will be too short.

So in this case, any number less than or equal to 21+27=48 could NOT be the length of the third side. Was this a multiple choice question?

Answer 3

using the rule that the sum of two sides of a triangle has exceed the thrid, the restriction is left to 27-21 = 6, 27+21 = 48
6

Answer 4

any number >= 48 or <= 6 because in any triangle one side is smaller than the sum of the other two and larger than their difference