If we know the sum and product of two numbers, what are they?

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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 \(y\).

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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.