A local market trader hangs a rectangular stall sign, shown in the diagram, with sides \(\sqrt{50}\) m and \(\sqrt{18}\) m. sqrt(50) msqrt(18) mDiagram not ...
Question 1 Report
A local market trader hangs a rectangular stall sign, shown in the diagram, with sides \(\sqrt{50}\) m and \(\sqrt{18}\) m.
Work out the area of the sign. Give your answer as an integer. (2)
Answer Details
The diagram gives the two side lengths of the rectangular sign as surds, \(\sqrt{50}\) m and \(\sqrt{18}\) m; the area of a rectangle is the product of its two sides, and surds multiply using \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\).
Multiplying the two labelled sides: \(\sqrt{50}\times\sqrt{18} = \sqrt{50\times18} = \sqrt{900}\). [1 mark]
Since \(900=30^{2}\), \(\sqrt{900}=30\), so the area of the sign is \(30\) m\(^{2}\). [1 mark]
Exam tip: multiplying the numbers under the roots first (\(50\times18=900\)) before taking the square root avoids having to simplify two separate surds.
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