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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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