Question

107. The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m, find its area :





please solve​

Answer 1

A N S W E R :

Given :

• The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m.

To Find :

• The area of triangular plot = ?

Solution :

• Let the sides of ∆ be 3x , 5x and 7x.
• Perimeter of ∆ = 300 m

Finding the sides of traingle :

→ Perimeter of ∆ = Sum of all sides of ∆

→ 300 = 3x + 5x + 7x

→ 300 = 15x

→ x = 300 ÷ 15

→ x = 20 m

Hence,the sides of ∆ will be :

• 3x = 3(20) = 60 m
• 5x = 5(20) = 100 m
• 7x = 7(20) = 140 m

Finding the semi perimeter of ∆ :

→ Semi Perimeter = Perimeter ÷ 2

→ Semi Perimeter = 300 ÷ 2

→ Semi Perimeter = 150 m

• Hence,the semi perimeter of ∆ is 150 m.

Now,let's calculate the area of triangle :

→ Area of ∆ = √s(s - a) (s - b) (s - c)

→ Area of ∆ = √150(150 - 60) (150 - 100) (150 - 140)

→ Area of ∆ = √150 × 90 × 50 × 10

→ Area of ∆ = √10 × 15 × 9 × 10 × 5 × 10 × 10

→ Area of ∆ = 10 × 10√5 × 3 × 3 × 3 × 5

→ Area of ∆ = 10 × 10 × 3 × 5 √3

→ Area of ∆ = 1500√3 m²

• Hence,the area of triangle is 1500√3 m².

Answer 2

Given:-

• Ratio of sides of Triangle = 3:5:7
• Perimeter of Triangle = 300m

Find:-

• Area of Triangle.

Solution:-

Let, The common multiple be x

Then, the sides of Triangle area 3x, 5x and 7x.

Now, using

↦ Perimeter of Triangle = a + b + c

where,

• a = 3x
• b = 5x
• c = 7x
• Perimeter of Triangle = 300m

• Substituting these values •

↬Perimeter = a + b + c

↬300 = 3x + 5x + 7x

↬300 = 15x

↬300/15 = x

↬20m = x

⠀⠀⠀⠀⠀_____________________________

❆Sides of Triangle:

✪ a = 3x = 3×20 = 60m

✪ b = 5x = 5×20 = 100m

✪ c = 7x = 7×20 = 140m

⠀⠀⠀⠀⠀_____________________________

Now, using

➯ s = (a + b + c)/2

where,

• a = 60m
• b = 100m
• c = 140m

• Substituting these values •

➩ s = (60 + 100 + 140)/2

➩ s = (300)/2

➩ s = 150m

Now, applying

↪Area of triangle = √{s(s - a)(s - b)(s - c)}

where,

• s = 150m
• a = 60m
• b = 100m
• c = 140m

• Substituting these values •

↣Area of triangle = √{s(s - a)(s - b)(s - c)}

↣Area of triangle = √{150(150 - 60)(150 - 100)(150 - 140)}

↣Area of triangle = √{150(90)(50)(10)}

↣Area of triangle = √(5×3×10×3×3×10×5×10×10)

↣Area of triangle = 5×3×10×10√(3)

↣Area of triangle = 1500√3m²

Hence, Area of the given Triangle is 1500√3m²