Algebra 7
3 marks · NormalA rectangular field has a perimeter of 38 m. The length is 4 m less than twice the width. Form a quadratic equation for the width, , and solve the equation to find the width. Show your reasoning.
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w^2 - 9w + 19 = 0; w = \frac{9 \pm \sqrt{17}}{2} m
Common mistakes: Mixing up relationships of length and width; Errors in setting up equation
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Translates context correctly, i.e., length = 2w-4, and sets up correct perimeter equation.
M2 · 1 mark · Forms and simplifies to quadratic equation: .
A1 · 1 mark · Finds both possible width values: .
Worked solution
Let width be m. Length = m.
Perimeter: .
.
, so and .
Alternate method (writing for length), sum w + 2w-4 = value, form quadratic equation: (on full expansion with L=2w-4).
Solving: