Algebra 7

2 marks · Hard

A rectangular plot has an area of 77 m². The length of the plot is 6 metres shorter than twice its width. Let the width of the plot be metres.

Write down a quadratic equation in for this situation and solve the equation to find the width of the plot.

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

7 m (±0.1)

Also accept: Width = 7 m

Common mistakes: Width given as negative; Wrong arrangement of quadratic equation; Calculation error in factorisation

Show mark scheme and worked solution

Marking points

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

A1 · 1 mark · Correct width found: m (rejecting negative value). (follow-through)

Worked solution

Let width = m. Length = m.

Expand:

Factorise:

So or . Width cannot be negative.

Width = 7 m.