• Answer of this question

    The perimeter of a right angle triangle is 30cms and it's hypotenuse is 13cms find the length of the other two sides
    Davneet Singh's image
    Davneet Singh

    Hi Balaji,

    Perimeter = 30 cm

    Hypotenuse = 13 cm

     

    Now,

    Perimeter  = Base + Height + Hypotenuse

    30 = Base + Height + 13

    30 - 13 = Base + Height

    Base + Height = 17

    Base = (17 - Height)

     

    Now, in a right angled Triangle

    (Hypotenuse)2 = (Base)2 + (Height)2

    (13)2 = (17 - Height)2 + (Height)2

    (13)2 = (17 - H)2 + (H)2

    169 = 172 + H2  - 2(17)H + H2

    169 = 2H2  - 34H + 289

    0 = 2H2  - 34H + 289 - 169

    2H2  - 34H + 120 = 0

    2(H2  - 17H + 60) = 0

    H2  - 17H + 60 = 0

    H2  - 12H - 5H + 60 = 0

    H(H - 12) - 5(H - 12) = 0

    (H - 5) (H - 12) = 0

    So, H = 5, 12

     

    If H = 5, Base = 17 - H = 17 - 5 = 12

    If H = 12, Base = 17 - H = 17 - 12 = 5

     

    Thus, the other two sides are 12 and 5

     


    Written on March 17, 2017, 12:10 p.m.