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Area - General Aptitude

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
Q1:

What is the area of a right-angled triangle?
I.  The perimeter of the triangle is 30 cm.
II.  The ratio between the base and the height of the triangle is 5 : 12.
 III.  The area of the triangle is equal to the area of a rectangle of length 10 cm.

A I and II only

B II and III only

C I and III only

D III, and either I or II only

E None of these

ANS:A - I and II only

From II, base : height = 5 : 12. Let base = 5x and height = 12x. Then, hypotenuse = (5x)2 + (12x)2 = 13x. From I, perimeter of the triangle = 30 cm.  5x + 12x + 13x = 30          x = 1. So, base = 5x = 5 cm, height = 12x = 12 cm.

 Area = 1 x 5 x 12 cm2 = 30 cm2.
2
Thus, I and II together give the answer. Clearly III is redundant, since the breadth of the rectangle is not given.  Correct answer is (A).