SOLUTION: A homeowner hires a mason to lay a brick border around a rectangular patio that measures 8ft by 10 ft. If the total area of the patio and border is 195 ft^2, what is the width of t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A homeowner hires a mason to lay a brick border around a rectangular patio that measures 8ft by 10 ft. If the total area of the patio and border is 195 ft^2, what is the width of t      Log On


   

Question 1008981: A homeowner hires a mason to lay a brick border around a rectangular patio that measures 8ft by 10 ft. If the total area of the patio and border is 195 ft^2, what is the width of the border?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If b is uniform width of brick border, x and y are the patio dimensions, A is the total area of combined patio and border, then you have

system%28x=8%2Cy=10%2CA=195%2Cb=unknownBorderWidth%29

Patio area only, xy
total combined, %28x%2B2b%29%28y%2B2b%29=A

Solve for b in highlight%28%28x%2B2b%29%28y%2B2b%29=A%29, and substitute the given values when you are ready. (Maybe the resulting quadratic expression equal to zero is factorable and maybe not.)

xy%2B2yb%2B2xb%2B4b%5E2-A=0
4b%5E2%2B%282x%2B2y%29b%2Bxy-A=0----you could keep going purely in symbols, but this is where you might be comfortable in substituting the given values for x,y,A, before continuing.