A music festival's rectangular main stage, shown in the diagram, has length \((3x-2)\) m and width \(x\) m. The perimeter of the whole stage is exactly 36 m...
Question 1 Report
A music festival's rectangular main stage, shown in the diagram, has length \((3x-2)\) m and width \(x\) m. The perimeter of the whole stage is exactly 36 m.
Work out the value of \(x\). (3)
Answer Details
The stage is a rectangle with length \((3x-2)\) m and width \(x\) m, so its perimeter is twice the sum of one length and one width; setting this expression equal to the given perimeter of 36 m gives an equation to solve for \(x\).
Perimeter \(=2[(3x-2)+x]=36\). [1 mark]
Expanding the bracket and simplifying: \(2(4x-2)=36\), so \(8x-4=36\). [1 mark]
Adding 4 to both sides gives \(8x=40\), so \(x=5\). [1 mark]
Checking: with \(x=5\), the length is \(3(5)-2=13\) m and the width is \(5\) m, giving a perimeter of \(2(13+5)=36\) m, which matches.
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