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Question
The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is
Options
70 cm2
140 cm2
210 cm2
420 cm2
Solution
We have to find the area of the given triangle.
Perimeter of triangle is 30 cm.
Let the radius of the circle be r.
We have,
Circumference of incircle=`88`
`2pi r=88`
` r=14`
Therefore,
`ar (ΔABC)=ar (ΔOAB)+ar (ΔOBC)+ar(ΔOAC)`
` = 1/2 (r)(AB+BC+CA)`
`= 1/2 (14)(30) cm^2`
`= 210 cm^2`
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