Can someone teach me how to do these types of math problems?

Question

Can someone teach me how to do problems like this one...


What is the range of values for x for a trianlge with sides 11, 8 and x. (How long or short can it be?) ______< x <_____

Answer 1

Each side of a triangle must be less than the sum of the other two sides. Otherwise the other two sides could not reach each other to close the triangle.

So that means:

(1) x plus the other smallest side, must be greater than the longest side:

x + 8 > 11
x > 3

(2) x must be less than the sum of the other two sides:

x < 8 + 11
x < 19

So the full range is:

3 < x < 19

If x <= 3, the side with length 11 is too long for the other two sides to reach each other. And if x >= 19, the side with length x is too long for the other two sides to reach each other.

Answer 2

Any two sides of a triangle must add up to MORE than the remaining side. This is caled the triangle inequality theorem.

In this case, x must be more than 3 (since 3+8=11) and less than 19 (since 11+8=19)

In other words, 3 < x < 19

Answer 3

the two shortest side of a triangle added together must be longer than the longest side. If 11 and 8 are the shortest sides then x could be any thing bigger than 19. If 11 is the longest side than x would have to be anything less than 3

Answer 4

I'm no expert but it would have to be

3 < x < 19

A side can't be shorter than one minus the other, nor can it be longer than the other two added together.

And if you're in doubt about which to subtract, just know that a side can never be negative.