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The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Its area is
- a)2598. 08m2
- b)5598. 08m2
- c)8598. 08m2
- d)6598. 08m2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its p...
Given:
Ratio of sides of the triangular plot = 3:5:7
Perimeter of the triangular plot = 300 m
To find:
Area of the triangular plot
Let the sides of the triangle be 3x, 5x, and 7x.
Perimeter of the triangle = sum of all three sides
3x + 5x + 7x = 300
15x = 300
x = 20
Therefore, the sides of the triangle are 3x = 60 m, 5x = 100 m, and 7x = 140 m.
Area of a triangle can be calculated using Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.
Let's calculate the semi-perimeter:
s = (60 + 100 + 140)/2
s = 300/2
s = 150
Now, we can calculate the area using Heron's formula:
Area = √(150(150-60)(150-100)(150-140))
Area = √(150*90*50*10)
Area = √(67500000)
Area ≈ 2598.08 m²
Therefore, the area of the triangular plot is approximately 2598.08 m², which corresponds to option A.
Ratio of sides of the triangular plot = 3:5:7
Perimeter of the triangular plot = 300 m
To find:
Area of the triangular plot
Let the sides of the triangle be 3x, 5x, and 7x.
Perimeter of the triangle = sum of all three sides
3x + 5x + 7x = 300
15x = 300
x = 20
Therefore, the sides of the triangle are 3x = 60 m, 5x = 100 m, and 7x = 140 m.
Area of a triangle can be calculated using Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides.
Let's calculate the semi-perimeter:
s = (60 + 100 + 140)/2
s = 300/2
s = 150
Now, we can calculate the area using Heron's formula:
Area = √(150(150-60)(150-100)(150-140))
Area = √(150*90*50*10)
Area = √(67500000)
Area ≈ 2598.08 m²
Therefore, the area of the triangular plot is approximately 2598.08 m², which corresponds to option A.
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Community Answer
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its p...
Let the side of a triangular plot be 3x,5x,7x.
perimeter=3x+5x+7x
300m=15x
x=20m
Side of a triangular field
Firstside=3x=3×20=60m secondside=5x=5×20=100m Thirdside=7x=7×20=140m
semiperimeter(S)=60+100+140/2=150m
Area if triangle =√s(s-a)(s-b)(s-c) =√150(150-60)(150-100)(150-140) =√150×90×50×10 =√6750000 =2,598.076m^2 =2,598.08m^2(Ans).
perimeter=3x+5x+7x
300m=15x
x=20m
Side of a triangular field
Firstside=3x=3×20=60m secondside=5x=5×20=100m Thirdside=7x=7×20=140m
semiperimeter(S)=60+100+140/2=150m
Area if triangle =√s(s-a)(s-b)(s-c) =√150(150-60)(150-100)(150-140) =√150×90×50×10 =√6750000 =2,598.076m^2 =2,598.08m^2(Ans).
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The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Its area isa)2598. 08m2b)5598. 08m2c)8598. 08m2d)6598. 08m2Correct answer is option 'A'. Can you explain this answer?
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