Question

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

Answer 1

Let the smaller side = x
then the sides will be = x , x+4 , 2x-6
perimeter = sum of the sides = x+x+4+2x-6 = 50
4x-2 = 50
4x = 52
x= 13
the sides are 13 , 17 , 20

Answer 2

Answer:

Let the Length of the smaller side = x cm

Length of the second side = (x + 4) cm

Length of the third side = (2x - 6) cm

Perimeter of a Triangle = 50 cm

According to Question now,

➳ Perimeter of triangle = Sum of all sides

➳ 50 = x + (x + 4) + (2x - 6)

➳ 50 = x + x + 4 + 2x - 6

➳ 50 = 4x - 2

➳ 4x = 50 + 2

➳ x = 52/4

➳ x = 13

Therefore,

Length of the smaller side = x = 13 cm

Length of the second side = (x + 4) = 13 + 4 = 17 cm

Length of the third side = (2x - 6) = 2(13) - 6 = 26 - 6 = 20 cm

_____________________

Now, we will find the Semi Perimeter of triangle :

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

➳ S = a + b + c/2

➳ S = 13 + 17 + 20/2

➳ S = 50/2

➳ Semi Perimeter = 25 cm

Now, we will find the area of triangle by using herons Formula :

$: \implies \sf \: Area = \sqrt{s(s - a) \: (s - b) \: (s - c) }$

$: \implies \sf \: Area = \sqrt{25(25 - 13) \: (25 - 17) \: (25- 20) }$

$: \implies \sf \: Area = \sqrt{25 \times 12 \times 8 \times 5 }$

$: \implies \sf \: Area = \sqrt{12000 }$

$: \implies \underline{ \boxed{ \sf \: Area = 20\sqrt{30 } \: cm }}$