The altitudes from the angular points A,B, and C on the opposite sides BC, CA and AB of `DeltaABC` are 210, 195 and 182 respectively. Then the value of a is ____

Answer

211.25

Explanation

`Delta = (1)/(2) xx 210 a = (1)/(2) xx 195b = (1)/(2) xx 182c`
`:. B = (210a)/(195) = (14)/(13) a, c = (210a)/(182) = (15)/(13) a`
Hence, `2s = a + (14a)/(13) + (15a)/(13) = ((13 + 14 + 15)a)/(13)`
or `s = (21a)/(13)`
Also `Delta = sqrt((21a)/(13) ((8a)/(13)) ((7a)/(13)) ((6a)/(13))) = (84a^(2))/(169)`

But `Delta = (1)/(2) xx 210a = (84a^(2))/(169)`
or `a = (105 xx 169)/(84) = (15 xx 169)/(12) = (845)/(4)`