## Problem Solving With Algebra

Problem solving typically involves using algebra to set up an equation or system of equations which must be solved to find the possible solutions. The simplest might be to find the value ofgiven the sides of a polygon in terms oftogether with a value for the perimeter.

Example: The perimeterof the trapezium below is found by adding up the lengths of all the sides:

Suppose we know thatWe havein terms ofso we can equate 99 andto obtain the equationand we solve this equation to obtain

Suppose we are told instead that the area is 66. The formula for the area of a trapezium isso given the expressions for the lengths of the sides on the diagram above we can find the area in terms of

We equate 66 and

We solve this equation:or

Onlyis possible sincemeans negative values for the lengths.