SOLUTION: A garden measuring 8 meters by 9 meters is to have a pathway installed all the way around it. This will increase the total are to 90 square meters. What will be the width of the pa

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A garden measuring 8 meters by 9 meters is to have a pathway installed all the way around it. This will increase the total are to 90 square meters. What will be the width of the pa      Log On


   

Question 963953: A garden measuring 8 meters by 9 meters is to have a pathway installed all the way around it. This will increase the total are to 90 square meters. What will be the width of the pathway ?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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

%28x%2B2u%29%28y%2B2u%29=A

xy%2B2yu%2B2xu%2B4u%5E2-A=0

4u%5E2%2B%282x%2B2y%29u%2Bxy-A=0

highlight_green%284u%5E2%2B%282x%2B2y%29u%2B%28xy-A%29=0%29
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%5E2%2B2%288%2B9%29u%2B%2872-90%29=0

4u%5E2%2B2%2A17%2Au-18=0

2u%5E2%2B17u-9=0, which is FACTORABLE...

%282u-1%29%28u%2B9%29=0

The uniform width, highlight%28u=1%2F2%29.