List of top Quantitative Ability and Data Interpretation Questions on Triangles asked in XAT

How many differently shaped triangles exist in which no two sides are of the same length, each side is of integral unit length and the perimeter of the triangle is less than 14 units?
In a triangle \(ABC\), \(AB=3\), \(BC=4\) and \(CA=5\). Point \(D\) is the midpoint of \(AB\), point \(E\) is on segment \(AC\) and point \(F\) is on segment \(BC\). If \(AE=1.5\) and \(BF=0.5\), then \(\angle DEF =\)
ABCD is a quadrilateral whose diagonals intersect at point P. The area of triangle APD is 27 and the area of triangle BPC is 12. If the areas of triangles APB and CPD are equal, then the area of triangle APB is
Directions: Each question below is followed by two statements, I and II. Decide whether the data in the statements is sufficient to answer the question, using these options:
(AA) Statement I alone is sufficient.
(BB) Statement II alone is sufficient.
(CC) Statements I and II together are sufficient, but neither alone is sufficient.
(DD) Either statement I alone or statement II alone is sufficient.
(EE) Statements I and II together are not sufficient.

The base of a triangle is 60 cm, and one of its base angles is \(60^{\circ}\). What is the length of the shortest side of the triangle?
I. The sum of the lengths of the other two sides is 80 cm.
II. The other base angle is \(45^{\circ}\).
ABC is a triangle with \(\angle BAC = 60^{\circ}\). A point P lies on one-third of the way from B to C, and AP bisects \(\angle BAC\). \(\angle APC = ?\)
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

ABC is a triangle with \(\angle B = 90^{\circ}\). What is the length of the side AC?
(A) D is the midpoint of BC and E is the midpoint of AB.
(B) AD = 7 and CE = 5.
Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

What is the maximum value of a/b?
(A) a, a + b and a + 2b are three sides of a triangle.
(B) a and b both are positive.
48. ABC is a triangle with \(\angle CAB = 15^{\circ}\) and \(\angle ABC = 30^{\circ}\). If M is the midpoint of AB, then \(\angle ACM = ?\)