Hi,
Please can someone expalin to be the relationship of the sides of a triange. I know the MGMAT states that the difference in two sides should be less that one side,that being the case, how can a triangle with sides 2,5,2 not be a triangle???

2. If vinegar and salt have ratio of 2:1 and vinegar and water have the ratio of 3:1 ,please how do you calculate the ratio of salt to water.

3.Finally,if an equilateral triangle is inscribed in a full circle(not in a semi circle) so that its arc length is 36,please how do you calculate the diameter of the circle.
Thanks!!!!

Hi tuichats,

When you post questions on different topics, please put them in different posts, not all in one.

Each single side of a triangle is shorter than the sum of the other two sides. It is also greater than the difference between them.

So if a,b,c are three sides of a triangle then
a < b + c
a > b - c

So your example of a 2,5,2 violates both these rules. Try drawing a triangle using your scale with these dimensions to visualize.

Ratio's is something I struggle with but I will have a go. According to your ratios, if I pick numbers:
Vinegar: 20ml
Salt: 10ml
Water: 20/3 ml (lets leave this in fractional form)

Now, Salt:Water = 10:20/3 = 3/2 or 3:2

This will be a bit difficult to explain without a diagram. I think we need to use the formula:

Angle cut by the arc/360 = Length of the arc/Circumference

The angle cut by each arc will be 120 as this is an equilateral triangle. Basically, if you draw a line from each vertex of the triangle to the center of the circle, the three angles formed at the center of the circle are all 120 degrees in measure.

120/360 = 36/Ï€d
=> d = 108/Ï€

Hope this helps

Regards

Sunil

Thanks Sunil,
But I need some clarification. Regarding the sides of the triangle, I believe the two rules must be fulfilled ,am I right?
Because 5>2-2.

In the 2nd question ,please can you explain how you got water as 20/3.

To explain this question further I will use another example
Peanut butter to jelly is,2:4 and Peanut butter and Mayo is 3:8
what is Jelly to Mayo.
Thanks!!

Hi tuichats,


Correct! In your case, the other rule is not being fulfilled because 5 is also greater than the sum of the other two sides. It has to be less than the sum of the other two sides.


I just picked numbers. I will try and explain using the next example.


I will pick a random number for one of these items and rest will follow from the ratios.
For example, lets say there is 20 grams of peanut butter. Then according to the ratio (P:J = 2:4), there is 40 grams of jelly. The other ratio is a bit complicated because of the presence of 3. We know peanut butter is 20 grams so mathematically we have the following equation:
3/8 = 20/X

Where X is the amount of Mayo in grams. Cross multiplying the two, we get X = 160/3 grams. Now, you have all the three values:
Peanut Butter: 20 grams
Jelly: 40 grams
Mayo: 160/3 grams

Therefore, Jelly:Mayo = Jelly/Mayo = 40/(160/3) = 3/4 or 3:4

Picking numbers is one way of doing this. I used this just to explain it to you. This can be done in a quicker way as follows:
P:J = 2:4 = 1:2
P:M = 3:8

At it stands, peanut butter is 1 unit in the ratio of P:J and 3 units in the ratio of P:M. To get J:M directly, we need to make peanut butter unit same in the two ratios. A simple manipulation is using a common multiplier. If we multiply both units of P:J ratio by 3, we can write the ratio of P:J as 3:6. Note that we are not changing the ratio as mathematically, its still 1:2.

Now we have
P:J = 3:6
P:M = 3:8

To get J:M,
P/M x J/P = J/M
3/8 x 6/3 = 6/8 = 3/4 or 3:4

Hope this makes it more clear

Regards

Sunil

Hi Sunil,
Thanks a lot.....
Really appreciate this!!!!
Thanks again!!!!

No problem at all

Great!

_________________
Jamie Nelson
ManhattanGMAT Instructor