Rectangular playing field has an area of 4000m². It is 40m longer than it is wide. If its width is w, solve the equation w(w + 40) = 4000 to find the length and width of the field to the nearest metre. Initially try w = 50?

Aug 6, 2018

$w = - 20 + 20 \sqrt{11}$

Explanation:

$w \left(w + 40\right) = 4000$
${w}^{2} + 40 w - 4000 = 0$

Completing the square:
${\left(w + 20\right)}^{2} - 400 - 4000 = 0$
${\left(w + 20\right)}^{2} - 4400 = 0$
${\left(w + 20\right)}^{2} = 4400$
$w + 20 = \pm \sqrt{4400} = \pm 20 \sqrt{11}$

As w is a length, it must be positive
$w = - 20 + 20 \sqrt{11}$