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The sides of the triangle are in the ratio 4:5:6 and then the perimeter of the triangle is 90m. then Area of the triangle.
- a)25
- b)45
- c)10
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The sides of the triangle are in the ratio 4:5:6 and then the perimete...
Since the ratio of sides is given as 4:5:6, let the side of the triangle be 4y,5y and 6y.
The perimeter is given as 90.Thus,
90=4y + 5y + 6y=15y
=> y=6.
Thus, the sides are 24,30,36.
Area of the triangle by Heron's formula=√s(s-a)(s-b)(s-c)=357.14 , where s is the semiperimeter and a,b,c are the sides of the triangle.
Since no options satisfy the answer, option D none of these is correct.
Most Upvoted Answer
The sides of the triangle are in the ratio 4:5:6 and then the perimete...
Understanding the Triangle's Sides
To find the area of a triangle with sides in the ratio of 4:5:6 and a perimeter of 90m, we first need to determine the lengths of the sides.
Finding the Side Lengths
- Let the sides of the triangle be represented as 4x, 5x, and 6x.
- The perimeter given is 90m, so we set up the equation:
4x + 5x + 6x = 90
- This simplifies to:
15x = 90
- Solving for x gives:
x = 6
- Therefore, the sides are:
- 4x = 24m
- 5x = 30m
- 6x = 36m
Calculating the Area Using Heron's Formula
To find the area of the triangle, we can use Heron's formula:
- First, calculate the semi-perimeter (s):
s = (24 + 30 + 36) / 2 = 45m
- Now, apply Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where a = 24m, b = 30m, c = 36m.
- Substituting the values:
Area = √[45(45 - 24)(45 - 30)(45 - 36)]
= √[45 × 21 × 15 × 9]
= √[113400]
- Calculating the area, we find:
Area = 337.5m² (approximately)
Conclusion
Since the answer options provided were a) 25, b) 45, c) 10, d) None of these, and the calculated area is approximately 337.5m², the correct answer is option 'D' - None of these.
To find the area of a triangle with sides in the ratio of 4:5:6 and a perimeter of 90m, we first need to determine the lengths of the sides.
Finding the Side Lengths
- Let the sides of the triangle be represented as 4x, 5x, and 6x.
- The perimeter given is 90m, so we set up the equation:
4x + 5x + 6x = 90
- This simplifies to:
15x = 90
- Solving for x gives:
x = 6
- Therefore, the sides are:
- 4x = 24m
- 5x = 30m
- 6x = 36m
Calculating the Area Using Heron's Formula
To find the area of the triangle, we can use Heron's formula:
- First, calculate the semi-perimeter (s):
s = (24 + 30 + 36) / 2 = 45m
- Now, apply Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where a = 24m, b = 30m, c = 36m.
- Substituting the values:
Area = √[45(45 - 24)(45 - 30)(45 - 36)]
= √[45 × 21 × 15 × 9]
= √[113400]
- Calculating the area, we find:
Area = 337.5m² (approximately)
Conclusion
Since the answer options provided were a) 25, b) 45, c) 10, d) None of these, and the calculated area is approximately 337.5m², the correct answer is option 'D' - None of these.
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The sides of the triangle are in the ratio 4:5:6 and then the perimeter of the triangle is 90m. then Area of the triangle.a)25b)45c)10d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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