The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
Let the smaller side be x cm
Larger side = (x + 4) cm
Third side = (2x-6) cm
Perimeter = 50 cm
⇒ x + (x + 4) + (2x-6) = 50
⇒ 4x-2 = 50
⇒ 4x = 52
⇒ x = 13
Therefore, smaller side = 13cm
Larger side = x + 4 = 13 + 4 = 17cm
Third side = 2x-6 = 2×13 – 6 = 26-6 = 20cm
a = 13, b = 17, c = 20
s = (a + b + c)/2
⇒ s = (13 + 17 + 20)/2 = 50/2 = 25.
Area(Δ) = √s(s-a)(s-b)(s-c)
⇒ Area(Δ) = √25(25-13)(25-17)(25-20)
⇒ Area(Δ) = √25×12×8×5
⇒ Area(Δ) = 20√30 cm2