The inradius in a right angled triangle with integer sides is r
If r = 4, the greatest perimeter (in units) is

Options

A. 96
B. 90
C. 60
D. 48

Answer

B

Explanation

Let a, b and `c(a lt b ltc)` be the sides of given triangle.
Also, `2r = a + b - c` ltbr when `r = 4` then, (a, b) = `(9, 40), (10, 24), (12, 16)`
`:.` Greatest perimeter `= 9 + 40 + 41 = 90` units
When r = 5 then `(a, b) = (11, 60) (12, 35) (15, 20)`
`:.` Greatest area `= (11 xx 60)/(2) = 330` sq unit