Algebra: Form and Solve Quadratic Equations

Worked Solution

Call the field's length l and its width w
From the question, l = w – 10
The field is rectangular so its area is l×w = (w – 10)w = 121
which expands to give the quadratic equation w² – 10 w – 121 = 0
Since the discriminant b² – 4 ac = 584 is not a perfect square, the roots are not integers so we use the formula to find the roots of the quadratic:

If a w2 + bw + c = 0 then w =

–b ± √(b2 – 4 ac) 2 a

For this question, a = 1, b = –10, c = –121 so the roots are

w =

10 + √(100 + 484) 2

= 17.08305 and w =

10 – √(100 + 484) 2

= -7.08305

The width is a positive value so the answer is
the width w is 17.083m,
the length l is w – 10 = 7.083m.