Interactive diagram

The sum and product of two numbers, \(x\) and \(y\), are \(10\) and \(12\) respectively. Form appropriate equations, plot [on graph paper] the corresponding graphs and hence obtain approximate values for \(x\) and \(y\).

The red rectangle has a horizontal side of length \(x\).

The vertical side has length \(y\), and the perimeter is fixed at \(20\). The area of the red rectangle is shown.