Maths-
General
Easy

Question

The lengths of the two sides of right triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm2. Find the perimeter of triangle

Hint:

Sides containing right angle are height and base.

The correct answer is: 24 cm


    It is given that difference between perpendicular and base = 2 cm
    i.e. b – h = 2  ⇒  b = 2 + h
    Now, Area of triangle = 24 cm2
    1 half cross times b cross times straight h= 24
    left parenthesis 2 plus h right parenthesis cross times h= 48
    h2 + 2h – 48 = 0
    h = fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    h = fraction numerator negative 2 plus-or-minus square root of 2 squared minus 4 left parenthesis negative 48 right parenthesis end root over denominator 2 end fraction equals fraction numerator negative 2 plus-or-minus square root of 196 over denominator 2 end fraction equals fraction numerator negative 2 plus-or-minus 14 over denominator 2 end fraction
    h = 6 , - 8
    Since, perpendicular is always positive so h = 6
    Base, B = 2 + 6 = 8
    Using Pythagoras theorem ,
    H2 = B2 + P2
    H2 = 82 + 62 = 64 + 36 = 100
    H = square root of 100 = 10 cm
    Perimeter of triangle = Sum of all sides
    = 8 + 10 + 6 = 24 cm

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