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Each of the questions below consists of a question and two statements numbered I and II are 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 :
Give answer 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.
Give answer 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.
Give answer c: If the data in Statement I alone or in Statement II alone are sufficient to answer the question.
Give answer d: If the data in both the Statements I and II are not sufficient to answer the question.
Give answer e: If the data in both the Statements I and II together are necessary to answer the question.
What is the area of the right-angled triangle?
I. Height of the triangle is three-fourth of the base.
II. Hypotenuse of the triangle is 5 metres.
Clearly, from each statement alone we cannot find the sides of the triangle, hence the area of triangle. Thus, by combining both statements, we get :
Let base = $$4x$$ m and height = $$3x$$ m
Hypotenuse = $$5=\sqrt{(4x)^2+(3x)^2}$$
=> $$16x^2+9x^2=5^2$$
=> $$25x^2=25$$
=> $$x^2=\frac{25}{25}=1$$
=> $$x=\sqrt{1}=1$$
Thus, base = $$4$$ m and height = $$3$$ m
=> Area of triangle = $$\frac{1}{2}\times4\times3=6$$ $$m^2$$
$$\therefore$$ Both statements together are sufficient.
=> Ans - (E)
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