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The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84 cm, then area of the triangle is :
- a)294 cm2
- b)290 cm2
- c)274 cm2
- d)252 cm2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of th...
Solution:
Given, the ratio of sides of a triangle is 3:4:5
Let the sides of the triangle be 3x, 4x and 5x
Perimeter of the triangle = 84 cm
Therefore, 3x + 4x + 5x = 84
=> 12x = 84
=> x = 7
So, sides of the triangle are 21 cm, 28 cm and 35 cm
Now, we have to find the area of the triangle.
Let us use Heron's formula to find the area of the triangle.
Heron's formula:
Area of triangle = √(s(s-a)(s-b)(s-c))
where a, b and c are the sides of the triangle and s = (a+b+c)/2 is the semi-perimeter.
Substituting the values, we get
s = (21+28+35)/2 = 42
Area of triangle = √(42(42-21)(42-28)(42-35))
= √(42*21*14*7)
= 294 cm²
Therefore, the area of the triangle is 294 cm²
Hence, option (A) is the correct answer.
Given, the ratio of sides of a triangle is 3:4:5
Let the sides of the triangle be 3x, 4x and 5x
Perimeter of the triangle = 84 cm
Therefore, 3x + 4x + 5x = 84
=> 12x = 84
=> x = 7
So, sides of the triangle are 21 cm, 28 cm and 35 cm
Now, we have to find the area of the triangle.
Let us use Heron's formula to find the area of the triangle.
Heron's formula:
Area of triangle = √(s(s-a)(s-b)(s-c))
where a, b and c are the sides of the triangle and s = (a+b+c)/2 is the semi-perimeter.
Substituting the values, we get
s = (21+28+35)/2 = 42
Area of triangle = √(42(42-21)(42-28)(42-35))
= √(42*21*14*7)
= 294 cm²
Therefore, the area of the triangle is 294 cm²
Hence, option (A) is the correct answer.
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The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84 cm, then area of the triangle is :a)294cm2b)290cm2c)274cm2d)252cm2Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84 cm, then area of the triangle is :a)294cm2b)290cm2c)274cm2d)252cm2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84 cm, then area of the triangle is :a)294cm2b)290cm2c)274cm2d)252cm2Correct answer is option 'A'. Can you explain this answer?.
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