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?

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Answer 1 · 2018-08-06T09:29:18

$w=-20+20sqrt11$

$w(w+40)=4000$
$w^2+40w-4000=0$

Completing the square:
$(w+20)^2-400-4000=0$
$(w+20)^2-4400=0$
$(w+20)^2=4400$
$w+20=+-sqrt4400=+-20sqrt11$

As w is a length, it must be positive
$w=-20+20sqrt11$