Aptitude - Area - Discussion
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.
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. |
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).
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.
The answer cannot be found out from the given assumptions.