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The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
- a)25 cm2
- b)42 cm2
- c)35 cm2
- d)70 cm2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The perimeter of a triangle is 28 cm and the inradius of the triangle ...
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
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The perimeter of a triangle is 28 cm and the inradius of the triangle ...
Given:
Perimeter of the triangle = 28 cm
Inradius of the triangle = 2.5 cm
To find:
Area of the triangle
Solution:
Let the sides of the triangle be a, b, and c.
Then, the perimeter of the triangle = a + b + c = 28 cm
Let s be the semi-perimeter of the triangle, i.e., s = (a + b + c)/2.
Then, we have s = 14 cm.
The inradius of the triangle is given by the formula:
r = Area of the triangle / s,
where r is the inradius and Area of the triangle is the area of the triangle.
Substituting the given values, we get:
2.5 = Area of the triangle / 14
Hence, the area of the triangle = 2.5 x 14 = 35 cm².
Therefore, the correct option is (c) 35 cm².
Perimeter of the triangle = 28 cm
Inradius of the triangle = 2.5 cm
To find:
Area of the triangle
Solution:
Let the sides of the triangle be a, b, and c.
Then, the perimeter of the triangle = a + b + c = 28 cm
Let s be the semi-perimeter of the triangle, i.e., s = (a + b + c)/2.
Then, we have s = 14 cm.
The inradius of the triangle is given by the formula:
r = Area of the triangle / s,
where r is the inradius and Area of the triangle is the area of the triangle.
Substituting the given values, we get:
2.5 = Area of the triangle / 14
Hence, the area of the triangle = 2.5 x 14 = 35 cm².
Therefore, the correct option is (c) 35 cm².
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The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?a)25 cm2b)42 cm2c)35 cm2d)70 cm2Correct answer is option 'C'. Can you explain this answer?
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