A triangular paddock has a road AB forming its hypotenuse. AB is 3 km long. The fences AC and CB are at right angles. If BC is 400 m longer than AC, find the area of the paddock in hectares.
By Pythagoras:
$\displaystyle AC^2 + CB^2 = AB^2$
but we know that $\displaystyle BC = AC + 0.4$ (if it is measured in kilometres).
So $\displaystyle AC^2 + (AC + 0.4)^2 = 3^2$
$\displaystyle AC^2 + AC^2 + 0.8AC + 0.16 = 9$
$\displaystyle 2AC^2 + 0.8AC - 9.84 = 0$
$\displaystyle AC^2 + 0.4AC - 4.92 = 0$.
Now you can use the Quadratic Formula to find $\displaystyle AC$.
Once you have AC, you will have the base and the height of the triangle, so you will be able to find its area.