the perimeter of a triangle is 50 cm. one side of the triangle is 4 cm longer than the smallest side and the third side is 6 cm less than twice the smallest side. find the area of the triangle.
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Let smaller side = a --------------- (i)
one side = a + 4 --------------- (ii)
third side = 2a - 6 --------------- (iii)
On solving (i),(ii),(iii) we get
= a + a + 4 + 2a - 6 =50
= 4a - 2 = 50
a = 13
Substituting a value in (i),(ii),(iii)
smaller side = 13
one side = 17
third side = 20
Perimeter = 20 + 17 + 13/2
= 50/2
= 25
Area = s(s-a)(s-b)(s-c)^1/2
= (25(25-13)(25-17)(25-20))^1/2
= 20(30)^1/2
= 20 root 30
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