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The perimeter of a triangle ABC right an...

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

A

1

B

2

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
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`
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