1. 

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

Answer: Option A

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).