Algebra 7

4 marks · Hard

A factory machines a rectangular sheet so that its length is 5 cm more than its width. The area of the sheet is 84 cm².

Let the width of the sheet be cm.

Form a quadratic equation for , solve it, and explain which solution is suitable for this context.

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.

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Width = 7 cm (since negative solutions are not suitable for a physical length)

Also accept: x = 7 is the only value that makes sense for the width

Common mistakes: Choosing the negative solution; Arithmetic mistake in equation setup or solution

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Forms correct quadratic equation: or equivalent.

M2 · 1 mark · Expands and rearranges equation to . (follow-through)

A1 · 1 mark · Solves quadratic correctly (), showing clear factorisation, quadratic formula, or other method. (follow-through)

B1 · 1 mark · States correctly that only the positive solution is suitable, explaining why the negative solution does not make physical sense.

Worked solution

Let width = cm, length = cm.

Factoring: ; or

In this context, width cannot be negative, so the width is 7 cm.