The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm l

1.	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.
Answer» Let the smaller side be = x cm Then, larger side = (x + 4) cm And, third side = (2x-6) cm Given that, 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 To find area of triangle, Let a = 13, b = 17, c = 20 s = (a + b + c)/2 ⇒ s = (13 + 17 + 20)/2 = 50/2 = 25. Area of triangle = √s(s-a)(s-b)(s-c) = √25(25-13)(25-17)(25-20) = √25×12×8×5 = 20√30 cm²

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.

Answer»

Let the smaller side be = x cm

Then, larger side = (x + 4) cm

And, third side = (2x-6) cm

Given that,

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

To find area of triangle,

Let a = 13, b = 17, c = 20

s = (a + b + c)/2

⇒ s = (13 + 17 + 20)/2 = 50/2 = 25.

Area of triangle = √s(s-a)(s-b)(s-c)

= √25(25-13)(25-17)(25-20)

= √25×12×8×5

= 20√30 cm²