Triangle Inequality

By:Erika Zumba Pd 4

How Triangle Inequality Works

Triangle Inequality Theorem

• The Triangle Inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

• For the triangle below:

• a + b > c b + c > a a + c > b

Problem#1The lenghts of two sides are 6 and 3. The length of the three side

may be:

To solve this question first you have to follow this easy steps:

Step1: Add 6 and 3 which gives you 9 and 9 would be the higher range

6 3

x

Step 2: Then you subtract 6 and 3 which gives you 3, 3 would be the lower range

Step 3: Write an inequality with x

Step 4Add the lower and higher range to the inequality

**So then the inequality would be 9<x<3**

The possible answer for x could be between 3 and 6 Credit-Erika

Zumba

S4

10

Problem #2

10-4= 610+4=14 <S<

Step 1: First you have to subtract 10-4 which equals 6 that would be The lower range

Step 2:Then you have to add 10+4 which equals 14 and that’s the higher range

Step 3: Write a inequality with s with less than signs

Step 4: Add the lower and higher range to the inequality

**So the third side has to be between 6 and 14**

To solve this problem its really easy:

6 14Credit-Ms.Mui

Problem #3 The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is

300 miles. Which could be the direct distance between city C and city A .

So lets analyze the question:

They are saying that between A and B is 200 miles. And they are also saying that between B and C is 300 miles. They want to know that what could be the distance between A and C.

A

B

C

300 miles200 milesFirst add 200 miles and 300 miles and you get 500 miles, 50 would be the higher range

Then subtract 300 miles with 200 miles and you get 100, 100 would be the lower range

After that, write an inequality with x, because x is the distance between A and C

Then add the 100 in the left side of the x and the 500 to the right of the x Mutiple Choice

1) 50 miles2) 350 miles3) 550 miles4) 650 miles

The inequality would like this 100<x<500

The possible answer could be between 100 and 500

So now look at the possible answers one of them is 50 miles but that the less than 100.The other choice is 550

miles but that answer is greater than 500, and so is 650. So that only leaves us with 350 being the answer.

Answer:350 miles

x

Credit-Ms.Mui

Useful Links http://regentsprep.org/Regents/math/geometry/GP7/LTriIneq.htm

http://www.mathopenref.com/triangleinequality.html