# Thread: Perimeter of a Triangle

1. ## Perimeter of a Triangle

I am preparing for my placement test for college, and I'm stuck on this perimeter problem (it's been awhile since high school):

Two sides of a triangle must be 8 m and 12 m. The perimeter must be at least 24 m, at most 39 m,. determine the length that can be used for the third side.

If you get it, please explain it to me...I feel like there isn't enough information to figure it.

2. Originally Posted by tigersblood
I am preparing for my placement test for college, and I'm stuck on this perimeter problem (it's been awhile since high school):

Two sides of a triangle must be 8 m and 12 m. The perimeter must be at least 24 m, at most 39 m,. determine the length that can be used for the third side.

If you get it, please explain it to me...I feel like there isn't enough information to figure it.
The length of those 2 sides together will be 20 metres. To get 24, we need at least 4 metres, and for 39 we need at least 19 metres. So the third side can be anything between 4 and 19 metres.

3. Hello, tigersblood!

Two sides of a triangle must be 8 m and 12 m.
The perimeter must be at least 24 m, at most 39 m.
Determine the length that can be used for the third side.
Let $\displaystyle x$ = length of the third side.

Then the perimeter is: .$\displaystyle x + 8 + 12 \:=\:x + 20$

The perimeter must be at least 24: .$\displaystyle x + 20 \:\geq \:24\quad\Rightarrow\quad x \:\geq \:4$

The perimeter must be at most 39: .$\displaystyle x + 20 \:\leq \:39\quad\Rightarrow\quad x \:\leq \:19$

Therefore, the third side must between 4 m and 19 m, inclusive.

4. Originally Posted by Soroban
Therefore, the third side must between 4 m and 19 m, inclusive.
Here is a question for that solution.
Can there be a triangle with sides of length 4,8, & 12?

5. Originally Posted by Plato
Here is a question for that solution.
Can there be a triangle with sides of length 4,8, & 12?
well, no. not unless we can think of a straight line as a very weird triangle where the sides overlap each other