Maths-
General
Easy

Question

The difference between the sides of right angle triangle containing the right angle is 7 cm and its area is 60 cm2 . Calculate the perimeter of triangle.

Hint:

Sides containing right angle are height and base.

The correct answer is: 40 cm


    It is given that difference between perpendicular and base = 7
    i.e. b – h = 7  ⇒  b = 7 + h
    Now, Area of triangle = 60 cm2
    1 half cross times b cross times h = 60
    left parenthesis 7 plus h right parenthesis cross times h = 120
    h2 + 7h – 120 = 0
    h2 +15h – 8h – 120 = 0
    h(h + 15)-8(h + 15) = 0
    (h + 15)(h – 8) = 0
    h = 8 , - 15
    Since, perpendicular is always positive so h = 8
    Base, B = 7 + 8 = 15
    Using Pythagoras theorem ,
    H2 = B2 + P2
    H2 = 152 + 82 = 225 + 64 = 289
    H = square root of 289 = 17 cm
    Perimeter of triangle = Sum of all sides
    = 17 + 8 + 15 = 40 cm

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