# Aptitude - Area - Discussion

Discussion Forum : Area - Data Sufficiency 2 (Q.No. 2)
Directions to Solve

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.
I and II only
II and III only
I and III only
III, and either I or II only
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.

Discussion:
3 comments Page 1 of 1.

Lekhaj Patha said:   7 years ago
What would be the case if we assume that the hypotenuse is base?

The answer cannot be found out from the given assumptions.

Hari said:   9 years ago
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.

Rakesh said:   9 years ago
From where did 13 x came?