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The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?
- a)32 cm2
- b)54 cm2
- c)67 cm2
- d)72cm2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimete...
It is given that the sides of a triangle are in the ratio 3 : 4 : 5.
Let the length of sides are 3x, 4x and 5x.
It's perimeter is 36 cm.
3x+4x+5x = 36
12x = 36
x = 3
The value of x is 3. The length of sides are 9, 12, 15.
It is an right angled triangle because the sum of squares of two smaller sides is equal to the square of larger sides.
92 + 122 = 152
81 + 144 = 225
Here, the length of hypotenuse is 15 cm.
The area of triangle is
1/2 x 9 x12
54 cm2
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Community Answer
The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimete...
Given, the sides of a triangle are in the ratio of 3 : 4 : 5 and its perimeter is 36 cm.
Let the sides of the triangle be 3x, 4x and 5x, where x is a positive constant.
Perimeter of the triangle = sum of all sides
36 = 3x + 4x + 5x
36 = 12x
x = 3
Therefore, the sides of the triangle are 9 cm, 12 cm, and 15 cm.
Now, to find the area of the triangle, we can use Heron's formula.
Heron's formula:
Area of triangle = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2 is the semi-perimeter of the triangle
Substituting the values of a, b, and c, we get:
s = (9+12+15)/2 = 18
Area of triangle = √(18(18-9)(18-12)(18-15))
= √(18 × 9 × 6 × 3)
= √(3² × 3² × 2² × 2² × 3)
= 3² × 2² × √3
= 36√3
≈ 62.35 cm²
Therefore, the area of the triangle is approximately 62.35 cm², which is closest to option B (54 cm²).
Let the sides of the triangle be 3x, 4x and 5x, where x is a positive constant.
Perimeter of the triangle = sum of all sides
36 = 3x + 4x + 5x
36 = 12x
x = 3
Therefore, the sides of the triangle are 9 cm, 12 cm, and 15 cm.
Now, to find the area of the triangle, we can use Heron's formula.
Heron's formula:
Area of triangle = √(s(s-a)(s-b)(s-c))
where s = (a+b+c)/2 is the semi-perimeter of the triangle
Substituting the values of a, b, and c, we get:
s = (9+12+15)/2 = 18
Area of triangle = √(18(18-9)(18-12)(18-15))
= √(18 × 9 × 6 × 3)
= √(3² × 3² × 2² × 2² × 3)
= 3² × 2² × √3
= 36√3
≈ 62.35 cm²
Therefore, the area of the triangle is approximately 62.35 cm², which is closest to option B (54 cm²).
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The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?a)32 cm2b)54 cm2c)67 cm2d)72cm2Correct answer is option 'B'. 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 the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?a)32 cm2b)54 cm2c)67 cm2d)72cm2Correct answer is option 'B'. 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 the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?a)32 cm2b)54 cm2c)67 cm2d)72cm2Correct answer is option 'B'. Can you explain this answer?.
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