# Aptitude - Area - Discussion

### Discussion :: Area - Data Sufficiency 2 (Q.No.2)

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.

2.

 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

Explanation:

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).

 Rakesh said: (Nov 12, 2014) From where did 13 x came?

 Hari said: (Jul 31, 2015) The hypotenuse root of (5x^2)+(12x^20). Root of 25x^2+144x^2, (5x5=25. 12x12=144). Root of (169)x^2 separate the root of x^2 & root of 169. Now root of x^2=x & root of 169=13. Finally 13x is came.

 Lekhaj Patha said: (Oct 10, 2017) What would be the case if we assume that the hypotenuse is base? The answer cannot be found out from the given assumptions.