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Discussion :: Area

  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.

  2. 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

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    Answer : Option A

    Explanation :

    From II, base : height = 5 : 12.

     

    Let base = 5x and height = 12x.

     

    Then, hypotenuse = \(\sqrt{(5X)^2}+{(12X})^2\)=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 =[\( \frac { 1 } { 2 }\)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).


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