Find Smallest Side of Triangle if Perimeter and Area is Given

The perimeter of a triangle is 30 cm and its area is 30 cm2. If the length of the largest side of the triangle is 13 cm, then what is the smallest side of the triangle?

  1. 5 cm
  2. 6 cm
  3. 4 cm
  4. 3 cm
Pushpendra Pal Dean Asked on 14th September 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 5 cm

    Explanation:-
    The perimeter of a triangle = 30 cm
    the area of a triangle = 30 cm2
    Then, ab/2 = 30
    ab = 30 x 2
    ab = 60 cm
    a = 60/b

    The  a  + b + 13 = 30
    a + b = 30 – 13
    a + b = 17          ………….. (1)
    Put the value of a = 60/b in equation (1),
    60/b + b = 17
    60 + b2 = 17 b
    b2 – 17 b + 60 = 0
    b2 – 12b – 5 b+ 60
    b (b – 12) – 5 (b – 12) = 0
    (b – 12) (b – 5) = 0
    b – 12 = 0 & b – 5 = 0
    b = 12 and b = 5

    Then, the sides of the triangle are 5, 7 and 13.

    Then, the smallest side of the triangle is 5.

    Hence, the answer is (1) 5 cm.

    Anurag Mishra Professor Answered on 15th September 2015.
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