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.
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:
but we know that (if it is measured in kilometres).
So
.
Now you can use the Quadratic Formula to find .
Once you have AC, you will have the base and the height of the triangle, so you will be able to find its area.