Question

The perimeter of the triangle is 154 cm . if it's sides are in the ratio 9 :7:6 find its area​

Answer 1

Given:

• The perimeter of the triangle is 154 cm.
• It's sides are in the ratio 9:7:6.

To find:

• The area of a triangle.

Solution:

Let,

a = 9x

b = 7x

c = 6x

• Perimeter of a triangle = a + b + c
• 154 = 9x + 7x + 6x
• 154 = 22x
• x = 154/22
• x = 77

Now,

⟹ a = 9 × 77

⟹ a = 693 cm

⟹ b = 7 × 77

⟹ b = 539 cm

⟹ c = 6 × 77

⟹ c = 462 cm

Now, find Semi-perimeter, S

• S = ( a + b + c )/2
• S = (693 + 539 + 462)/2
• S = 1694/2
• S = 847

• Area of triangle = √s(s - a ) ( s - b ) ( s - c )
• Area of triangle = √847( 847 - 693 ) ( 847 - 539 ) ( 847 - 462 )
• Area of triangle = √847 × 154 × 308 × 385
• Area of triangle = √7 × 11² × 2 × 7 × 11 × 2² × 7 × 11 × 5 × 7 × 11
• Area of triangle = √7² × 11² × 2 × 11² × 2² × 7² × 5 × 11
• Area of triangle = (7 × 11 × 11 × 2 × 7)√2 × 11 × 5
• Area of triangle = 11858√110
• Area of triangle = 11858√110 cm²

∴ The area of a triangle = 11858√110 cm²

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Answer 2

Answer:

• Area of Triangle is 1027.83cm²

Step-by-step explanation:

Given :

• Perimeter of Triangle = 154cm
• Ratio of its sides = 9:7:6

To Find :

• Area of Triangle

Solution :

Let,

• First Side of Triangle = 9b
• Second Side of Triangle = 7b
• Third Side of Triangle = 6b

According to the Question :

⠀⟶⠀Perimeter = Sum of all Sides

⠀⟶⠀154 = 9b + 7b + 6b

⠀⟶⠀154 = 9b + 13b

⠀⟶⠀154 = 22b

⠀⟶⠀154/22 = b

⠀⟶⠀7 = b

Therefore :

• First Side = 9b
• First Side = 9 × 7
• First Side = 63cm

• Second Side = 7b
• Second Side = 7 × 7
• Second Side = 49cm

• Third Side = 6b
• Third Side = 6 × 7
• Third Side = 42cm

Now finding the semi perimeter :

⠀⟶⠀Semi Perimeter = a + b + c/2

⠀⟶⠀Semi Perimeter = 63 + 49 + 42/2

⠀⟶⠀Semi Perimeter = 63 + 91/2

⠀⟶⠀Semi Perimeter = 154/2

⠀⟶⠀Semi Perimeter = 77cm

Now applying Heron's Formula :

⠀⟶⠀Area = √s (s - a) (s - b) (s - c)

⠀⟶⠀Area = √77(77 - 63)(77 - 49)(77 - 42)

⠀⟶⠀Area = √77 × 14 × 28 × 35

⠀⟶⠀Area = √1078 × 980

⠀⟶⠀Area = √10,56,440

⠀⟶⠀Area = 1027.83cm²

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