The inradius in a right angled triangle with integer sides is r If r = 5, the greatest area (in sq. units) is

Monjur Alahi

The inradius in a right angled triangle with integer sides is r
If r = 5, the greatest area (in sq. units) is
A. 150
B. 210
C. 330
D. 450


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Salim Ahmed Kawsar

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Correct Answer - C
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

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