Algebra 7
3 marks · NormalA rectangular garden has a length that is 2 m greater than its width. The area of the garden is 48 m^2.
(a)[1 mark]
Form a quadratic equation for the width of the garden, .
(b)[2 marks]
Solve the equation to find the width of the garden.
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(a) w(w+2)=48 or w^2+2w-48=0
(b) w=6 m
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Marking points
M1 (a) · 1 mark · Sets up correct quadratic: or .
M2 (b) · 1 mark · Attempts correct solution method (factorising or quadratic formula or completing square).
A1 (b) · 1 mark · Width m stated clearly (ignore negative root).
Worked solution
Let width be m. Length = m.
Area = .
Quadratic: .
Factorise: , so (since width is positive).