## Quadratics and Area

Many problem solving questions involve simultaneous equations or quadratics.

Example: The height of a rectangle is 2 cm longer than the base. If the area is 48 cm ^{2 } find the length of the base.

If the base isthe height is

The area isand equating this to 48 givesExpanding the brackets and subtracting 48 gives

We can factorise this expression to giveEquating each factor to 0 gives

We cannot have a negative length soThis leaves