Question 963953
A garden measuring x meters by y meters is to have a pathway installed all the way around it. This will increase the total are to A square meters. What will be the width u of the pathway ?


x and y are KNOWN variables, 
x=8
y=9
A=90
u=UNKNOWN width


{{{(x+2u)(y+2u)=A}}}


{{{xy+2yu+2xu+4u^2-A=0}}}


{{{4u^2+(2x+2y)u+xy-A=0}}}


{{{highlight_green(4u^2+(2x+2y)u+(xy-A)=0)}}}
You can continue solving in symbolic form completely if you have a few or several examples like the given problem, but for just one example, this would be the best place to substitute the given values and solve for u.


{{{4u^2+2(8+9)u+(72-90)=0}}}


{{{4u^2+2*17*u-18=0}}}


{{{2u^2+17u-9=0}}}, which is FACTORABLE...


{{{(2u-1)(u+9)=0}}}


The uniform width, {{{highlight(u=1/2)}}}.