Question 130616

The area of the path is (draw the sketch):
2*x*(40+2x)+2*25*x  simplifying
80x+4x^2+50x  and this equals

4x^2+130x------------Area of the path

Area of the playground=40*25=1000 sq m
Area of the path=1426-1000=426 sq m

So----4x^2+130x=426  subtract 426 from both sides

4x^2+130x-426=0   divide each term by 2

2x^2+65x-213=0  ----------------quadratic in standard form--solve using the quadratic formula

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-65 +- sqrt( 65^2-4*2*(-213) ))/(2*2) }}} 
{{{x = (-65 +- 77)/(4) }}}
Disregard the negative value for x; in this case, lengths are positive
So:
{{{x=12/4=3}}} ft-----------------width of the path

CK
(25+6)(40+6)=1426
31*46=1426
1426=1426

Hope this helps---ptaylor