(x + 4) mx mDiagram not to scale© EAGLE BEACON GLOBAL A farmer is planning a new rectangular field next to the river, shown in the diagram, with length \((x...
Question 1 Report
A farmer is planning a new rectangular field next to the river, shown in the diagram, with length \((x+4)\) m and width \(x\) m. The area of the field must be exactly \(45\) m\(^2\).
Form and solve an equation to find \(x\), where \(x \gt 0\). (3)
Answer Details
The area of the rectangular field is length \(\times\) width; setting this product equal to the given area produces a quadratic equation, and the physical restriction \(x\gt0\) then selects the valid root.
Area \(=x(x+4)=45\), which expands to \(x^{2}+4x-45=0\). [1 mark]
Factorising: two numbers multiplying to \(-45\) and adding to \(4\) are \(9\) and \(-5\), so \((x+9)(x-5)=0\), giving \(x=-9\) or \(x=5\). [1 mark]
Since \(x\gt0\), a width cannot be negative, so \(x=5\) m. [1 mark]
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