Question

the perimeter of a triangle is 50cm one side of a triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side find the area of the triangle
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Answer 1

Answer:

Side1 = 13, side2 = 17, side3 = 20

Step-by-step explanation:

Perimeter = 50 cm

Let the smaller side be x

3rd side z = 2x - 6 cm

Relationship between other two sides: y = x+4

Sides are: z, x & y

After substituting: 2x - 6, x, x+4

Sum of these = perimeter

2x - 6 + x + x + 4 = 50

4x - 2 = 50

4x = 52

x = 13

y = 17

z = 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 :

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

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

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

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

$: \implies \underline{ \boxed{ \sf \: Area = 20\sqrt{30 } \: cm^2}}$