The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. then area of triangle is =?
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Answered by
112
Perimeter of a triangle ABC = 30 cm
let, AB = x, BC = y, CA = z
=> x + y + z = 30 ………..(1)
Circumference of incircle with incentre O , of tri ABC = 2 pi r = 88
2pi r = 88
=> pi r = 44
=> r = (44/ 22)*7
=> r = radius of the incircle = 14 cm
Now, we calculate the area of triangle ABC =
ar( tri OAB) + ar( tri OBC) + ar( ( tri OCA)
= (0.5*x* 14) + (0.5*y* 14) + (0.5*z* 14)
= 7x + 7y + 7z
= 7( x+y+ z)
= 7 * 30 ( by equation 1)
= 210
Area of tri ABC = 210 cm²
let, AB = x, BC = y, CA = z
=> x + y + z = 30 ………..(1)
Circumference of incircle with incentre O , of tri ABC = 2 pi r = 88
2pi r = 88
=> pi r = 44
=> r = (44/ 22)*7
=> r = radius of the incircle = 14 cm
Now, we calculate the area of triangle ABC =
ar( tri OAB) + ar( tri OBC) + ar( ( tri OCA)
= (0.5*x* 14) + (0.5*y* 14) + (0.5*z* 14)
= 7x + 7y + 7z
= 7( x+y+ z)
= 7 * 30 ( by equation 1)
= 210
Area of tri ABC = 210 cm²
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64
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