The area of a right triangle is 6864 sq. units. If the ratio of its legs is `143 : 24`, then the value of r is ______

Answer

22

Explanation

`(a)/(b) = (143)/(24) rArr (a)/(143) = (b)/(24) =k` (let)
Area of triangle `(Delta) = (1)/(2) ab = 6864`
or `143 k xx 24k = 2 xx 6864`
or `12k^(2) xx 143 = 6864`
or `k^(2) = 4`
or `k = 2`
`rArr a = 286, b = 48`
Now `c^(2) = 48^(2) + (286)^(2) = 290^(2)`
or `c = 290`
Hence, the radius of the circle inscribed in the triangle is given by
`r = (Delta)/(s) = 22`