bblast wrote:anshumishra wrote:iridebikes wrote:In isoceles triangle MNP, MN=MP and NP=6. Which of the following could be the length of side MN?
I. 2
II. 6
III. 12
A) II only
B) III only
C) I and II only
D) II and III only
E) I,II, and III
I was under the impression that for any two sides, the shortest side must be greater than the difference between the longest/shortest. Thanks guys.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
So, 2 is not possible.
6 and 12 are possible.
D
Anshu i got to the answer, but sorry for bothering you again.
for triangles' side length i remember 2 properties :
a+b > c and
|a-b| < c (mod of difference of 2 sides is always less than the 3rd side)
for isosceles if I apply the second property, the length comes as |6-6| < 6. is this correct (i mean 6-6 = 0) ?
No problem bblast.
Here you have been assuming that a and b are equal (to 6) and you are trying to find the range for c. If that would have been the case, then it is right. If in a triangle two sides are equal to 6, the third side can take any value greater than 0 (and less than 6+6).
But, here the case is different. We are given one side equal to 6 and want to find range for the other two sides which are equal.
Lets say, a = b = x
c = 6
Using your rule :
Find the lower limit of x:
x+x > 6
=> x> 3 ... we found the lower limit
Find the upper limit of x:
If i use x-x < 6 => 0< 6 ,
that is an identity so it means any value of x is good.
Combining the two:
x>3
Any value of x satisfying this can be the two sides.
.
