The perimeter of a triangle ABC right angled at C is 70 and the inradius is 6, then `|a-b|=`

Options

A. 1
B. 2
C. 8
D. 9

Answer

A

Explanation

We know `Delta =sr=(70//2)xx6=210`
`rArr (1//2)ab=210rArr ab=420`
Now `(a+b)^(2)=(70-c)^(2)`
`rArr a^(2)+b^(2)+2ab=4900-140c + c^(2)`
`rArr c=(4900-2xx420)/(140)=29 " " [because a^(2)+b^(2)=c^(2)]`
`rArr (a-b)^(2)=a^(2)+b^(2)-2ab=c^(2)-2ab=841-840=1`