Latest Elitmus Aptitude Question SOLUTION: is perimeter of triangle > 30? a,b,c are sides of triangle. a. a-b=15; b. area of triangle 15.

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(#M40164763) ELITMUS Numerical Ability question Data sufficency asked on 20 aug 2017. Keep an EYE

is perimeter of triangle > 30? a,b,c are sides of triangle.
a. a-b=15;
b. area of triangle 15.

Asked In Elitmus raj (6 years ago)

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suryanemala  (6 years ago)

Statement 1: a-b = 15.
The third side of a triangle must be greater than the difference between the lengths of the other 2 sides.
Thus:
c > a-b
c > 15.

Since a-b = 15, a = b+15.
Thus:
Perimeter = a + b + c = (b+15) + b + (more than 15) = 2b + (more than 30).
SUFFICIENT.

Statement 2: area = 50
Given a triangle with perimeter p, the maximum possible area will be yielded if the triangle is EQUILATERAL.
Thus, if p=30, then the maximum possible area will be yielded if each side = 10.
The area of an equilateral triangle = (s²√3)/4.
If p=30 and s=10, then the area = (10²√3)/4 = 25√3 = less than 50.
Implication:
The maximum possible area of a triangle with a perimeter of 30 is LESS THAN 50.
Since statement 2 requires that the area be EQUAL TO 50, the perimeter of the triangle must be GREATER THAN 30.
SUFFICIENT.

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ojasmitha reddy  (4 years ago)

sum of any two sides is greater than the third side
say a+b+c=30
given a-b=15
a=15+b
15+2b+c=30
c must be greater than 15 and hence the permitre also must be greater than 15

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