Algebra 3
4 marks · HardA rectangular flower bed has a width that is 5 m less than its length. The area is 84 m².
Let the length of the bed be m. Form a quadratic equation for and solve it to find the dimensions of the flower bed.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Length: 12 m, Width: 7 m
Also accept: Length: 7 m, Width: 12 m (with variable definitions swapped and justified in the working)
Common mistakes: Mixing up length and width; Sign errors forming quadratic equation
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Let length be x m; width is x - 5. Forms area expression: x(x−5) = 84
M1 · 1 mark · Expands and rearranges to a quadratic equation: x^2 − 5x − 84 = 0 or equivalent (follow-through)
A1 · 1 mark · Solves quadratic correctly, using appropriate method: x = 12 or x = -7 (follow-through)
A1 · 1 mark · Rejects negative solution and gives correct dimensions: length 12 m, width 7 m (follow-through)
Worked solution
Let the length be m, so the width is m.
Area:
Factorise:
So or . Negative length is not possible, so m.
Width = 12 - 5 = 7 m.
The flower bed is 12 m by 7 m.