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The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?
- a)10 cm
- b)30 cm
- c)45 cm
- d)60 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The area of a triangle is 150 cm2and its sides are in the ratio 3 : 4 ...
Here's the solution to your question:
Let coefficient of ratios be X
a = 3x
b = 4x
c = 5x
Using Heron's Formula,
s = (3+4+5)x2 = 12x/2 = 6x
Now,
a = 5*3 = 15 cm
b = 5*4 = 20 cm
c = 5*5 = 25 cm
Perimeter = 15+20+25 = 60 cm
So, Correct Answer is Option D.
You can learn more about Heron's formula by going through the link:
You can learn more about Heron's formula by going through the link:
Most Upvoted Answer
The area of a triangle is 150 cm2and its sides are in the ratio 3 : 4 ...
Given:
Area of triangle = 150 cm²
Sides are in the ratio 3:4:5
To find: Perimeter of the triangle
Solution:
Let the sides of the triangle be 3x, 4x and 5x
We know that the area of a triangle is given by:
Area = 1/2 * base * height
Let the base be 3x and the height be h.
150 = 1/2 * 3x * h
h = 100/x
Using the Pythagorean theorem, we have:
(3x)² + (h)² = (4x)²
9x² + (100/x)² = 16x²
7x² = (100/x)²
x⁴ = 100²/7
x² = 100/√7
x = 10/√7
Therefore, the sides of the triangle are:
3x = 30/√7
4x = 40/√7
5x = 50/√7
The perimeter of the triangle is:
Perimeter = 3x + 4x + 5x = 12x = 120/√7
Approximately, the perimeter is 60 cm.
Hence, option D is the correct answer.
Area of triangle = 150 cm²
Sides are in the ratio 3:4:5
To find: Perimeter of the triangle
Solution:
Let the sides of the triangle be 3x, 4x and 5x
We know that the area of a triangle is given by:
Area = 1/2 * base * height
Let the base be 3x and the height be h.
150 = 1/2 * 3x * h
h = 100/x
Using the Pythagorean theorem, we have:
(3x)² + (h)² = (4x)²
9x² + (100/x)² = 16x²
7x² = (100/x)²
x⁴ = 100²/7
x² = 100/√7
x = 10/√7
Therefore, the sides of the triangle are:
3x = 30/√7
4x = 40/√7
5x = 50/√7
The perimeter of the triangle is:
Perimeter = 3x + 4x + 5x = 12x = 120/√7
Approximately, the perimeter is 60 cm.
Hence, option D is the correct answer.
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Community Answer
The area of a triangle is 150 cm2and its sides are in the ratio 3 : 4 ...
The answer will come 60 cm
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