Ratio

[easilyconfuzzeled]

I have many problems in my geometry that I need help with. The main problem I am having problems with is this;

The sides of a triangle are in the ratio 2:3:4. If the measure of the shortest side is 12 centimeters, what is the longest side?
Ive been trying to figure out how to answer this for a while now and I don't even know where to begin! I'm getting really frustrated with this! :evil: Please help me!

 

[Mrspi]

I have many problems in my geometry that I need help with. The main problem I am having problems with is this;

The sides of a triangle are in the ratio 2:3:4. If the measure of the shortest side is 12 centimeters, what is the longest side?
Ive been trying to figure out how to answer this for a while now and I don't even know where to begin! I'm getting really frustrated with this! :evil: Please help me!

If you let 2x = the shortest side, 3x = the "middle length" side, and 4x = the longest side, the three sides will be in the desired ratio. 2x:3x:4x = 2:3:4

Now...you are told that the shortest side is 12 cm. So,
2x = 12

Solve that for x. Once you know the value of x, it should be easy to find the length of the longest side.

There are other ways to approach this problem, but this is the one I prefer, because it lends itself to many other kinds of questions. For example, suppose you were told that the perimeter of the triangle was 45 inches, and were asked to find the lengths of all three sides. Since we've represented the three sides as 2x, 3x and 4x (in order for them to be in the stipulated ratio), the perimeter would be 2x + 3x + 4x, or 9x...and if the perimeter is 45, then 9 x = 45. You could solve this for x, and use the value of x to find the length of each of the sides.

 

[easilyconfuzzeled]

Thank you so much! I was getting ready to throw a fit! Its a lot easier to figure out what your doing when you put x in the problem! If they would have put that in the problem i wouldn't have needed help! :lol: