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In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle
Answer & Solution
Correct Answer:
Option
B
According to question,
AB + BC = 12 cm
BC + CA = 14 cm
CA + AB = 18 cm
2(AB + BC + CA) = 44 cm
AB + BC + CA = $$\frac{{44}}{2}$$ cm
AB + BC + CA = 22 cm
Perimeter of triangle = 22 cm
Perimeter of triangle = Perimeter of circle
22 = 2πr
2 × $$\frac{{22}}{7}$$ × r = 22
r = $$\frac{7}{2}$$ cm
AB + BC = 12 cm
BC + CA = 14 cm
CA + AB = 18 cm
2(AB + BC + CA) = 44 cm
AB + BC + CA = $$\frac{{44}}{2}$$ cm
AB + BC + CA = 22 cm
Perimeter of triangle = 22 cm
Perimeter of triangle = Perimeter of circle
22 = 2πr
2 × $$\frac{{22}}{7}$$ × r = 22
r = $$\frac{7}{2}$$ cm
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