1. ## Problem solving with Quadratics

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.

2. Originally Posted by Tessarina
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:

$AC^2 + CB^2 = AB^2$

but we know that $BC = AC + 0.4$ (if it is measured in kilometres).

So $AC^2 + (AC + 0.4)^2 = 3^2$

$AC^2 + AC^2 + 0.8AC + 0.16 = 9$

$2AC^2 + 0.8AC - 9.84 = 0$

$AC^2 + 0.4AC - 4.92 = 0$.

Now you can use the Quadratic Formula to find $AC$.

Once you have AC, you will have the base and the height of the triangle, so you will be able to find its area.