Instructions

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and
(A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
(B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
(C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
(D) If the data given in both statements I and II together are not sufficient to answer the question and
(E) If the data in both statements I and II together are necessary to answer the question.

Question 149

# What is the area of right angle triangle ?I.Height of right-angled triangle is ¾ th of its baseII.Length of the diagonal of the right angle triangle is 5 meters

Solution

I : Let base of the triangle = $$4x$$ m

=> Height of triangle = $$\frac{3}{4} \times 4x = 3x$$ m

There is no other info, so I alone is insufficient.

Similarly, II alone is also insufficient.

Combining both statements, and using pythagoras theorem, we get :

=> $$(3x)^2 + (4x)^2 = (5^2)$$

=> $$9x^2 + 16x^2 = 25$$

=> $$x^2 = \frac{25}{25} = 1$$

=> $$x = \sqrt{1} = 1$$

=> Base = 4 m and height = 3 m

$$\therefore$$ Area of triangle = $$\frac{1}{2} \times 3 \times 4 = 6 m^2$$

Thus, both statements together are sufficient.