OE
What kind of an answer will the question fetch?The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?The data is sufficient if we are able to get a DEFINTE YES or DEFINITE NO as the answer.
If the statements independently or together do not provide a DEFINITE YES or DEFINITE NO, the data is NOT sufficient.
What do we know from the question stem?The question stem states that a, b, and c are the measures of the sides of a triangle.
Key properties of a triangleIf a, b, and c are the measures of the sides of a triangle, and if 'a' is the longest side of the triangle, then
i) the triangle is acute angled if \(a^2\) < \(b^2\) + \(c^2\)
ii) right angled if \(a^2\) = \(b^2\) + \(c^2\)
iii) obtuse angled if \(a^2\) > \(b^2\) + \(c^2\)
Quote:
Statement 1: Triangle with sides \(a^2\), \(b^2\), \(c^2\) has an area of 140 sq cms.
The statement provides us with one valuable information: we can form a triangle with sides \(a^2\), \(b^2\), \(c^2\)
For any triangle we know that sum of two sides is greater than the third side.
So, we can infer that \(a^2\) < \(b^2\) + \(c^2\).
The inequality above is the condition to be met if the triangle with sides a, b and c were to be an acute triangle.
So Statement 1 itself is sufficient.
Quote:
Statement 2: Median AD to side BC is equal to altitude AE to side BC.
Equilateral and Isosceles triangle propertiesi) For an equilateral triangle, medians to the sides of the triangle are the corresponding altitudes. i.e., the median and altitude of all 3 sides are coincident lines.
ii) For an isosceles triangle, the median to the side whose measure is different is the altitude to that side. i.e., only one median is the same as the altitude.
From statement 2, we can infer that the triangle is either equilateral or isosceles.
An equilateral triangle is definitely an acute angled triangle. However, an isosceles triangle need not be an acute angled triangle.
So Statement 2 is not sufficient
gmatbusters has explained it well