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).
The answer cannot be found out from the given assumptions.
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.