Problem solving with Quadratics

**Tessarina** · February 16th 2010, 10:05 PM

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.

**Prove It** · February 17th 2010, 01:46 AM

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.

**HallsofIvy** · February 17th 2010, 03:12 AM

Why was this particular question moved from "Algebra and Prealgebra" while the other questions about quadratic equations were left?

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