MHB Solve Trig Word Problem: Acre Parcel Sides 180 & 240 ft

[karush]

View attachment 4641
A one acre parcel has 2 sides 180 ft and 240 ft intersecting at a right angle.
the other side adjacent to the 180 ft is 200 ft what is the length of the 4th side.

by Pythagorean theorem $BD = 300$

so triangle ABD = $21600 \ ft^2$
thus triangle DBC = $21960 \ ft^2$

so 21960 = (1/2)(300)(h) then h=146.4

$$\sqrt{{200}^{2}{}-146.4^2}=136.26$$

$300-136.36 =163.74$

so by Pythagorean theorem $BC$ or the 4th side $\approx$ $219.64 ft$

not sure this is correct, saw another proposed way to do this
using Heron's theorem but after trying it was ?

 

[Opalg]

That looks good. I agree with your answer, and I don't see any simpler method for finding it.