CocoOwen

Using Herons Formula,

sqrt(s(s-AB)(s-BC)(s-CA)) = sqrt(17(17-15)(17-9)(17-10)) = sqrt(17 * 2 * 8 * 7) = sqrt(1904) = 4√119

Then, you solve for the altitudes:

BC_a = (2 * A) / BC = (2 * 4√119) / 9 = (8√119) / 9

CA_a = (2 * A) / CA = (2 * 4√119) / 10 = (8√119) / 10 = (4√119) / 5

AB_a = (2 * A) / AB = (2 * 4√119) / 15 = (8√119) / 15

The shortest one is (8√119) / 15.

I think you are wrong because when 2i^2=-2

(3+2i)/(1-i)

= ((3+2i)*(1+i))/((1-i)*(1+i))

= (3+3i+2i+2i^2)/(1+i-i-i^2)

= (3+(-2)+5i)/2

= (1+5i)/2

(1+5i)/2 or 1/2+5/2i

1/(1*4)+1/(4*7)+1/(7*10)

= 1/4+1/28+1/70

Using the common denominator of 140:

35/140+5/140+2/140

= 42/140

= 3/10

3/10 or 0.3

The answer was $\frac32$