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?


The perimeter of the triangle is 30 cm.


The ratio between the base and the height of the triangle is 5 : 12.


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

Answer: Option A


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.

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.

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