SOLUTION: You are planning a rectangular garden. Its length is twice its width. You want a walkway 2 ft wide around the garden. a.Write an expression for the area of the garden and walk.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: You are planning a rectangular garden. Its length is twice its width. You want a walkway 2 ft wide around the garden. a.Write an expression for the area of the garden and walk.       Log On


   

Question 67338This question is from textbook Prentice Hill Mathematics
: You are planning a rectangular garden. Its length is twice its width. You want a walkway 2 ft wide around the garden.
a.Write an expression for the area of the garden and walk.
b.Write an expression for the area of the walk only.
c.You have enough gravel to cover 76 ft^2(squared) and want to use it all on the walk. How big should you make the garden? This question is from textbook Prentice Hill Mathematics

Answer by raghu_pratoori(2) About Me  (Show Source):
You can put this solution on YOUR website!
Let width(w)of rectangular garden be xft.
therefore length(l) of garden=2xft
a.l of garden and walk=(2x+2)ft
w of garden and walk=(x+2)ft
area of garden and walk=(2x+2)(x+2)=2x^2+2x+4x+4=(2x^2+6x+4)ft^2
b.area of only walk=area of garden and walk-area of garden
area of garden=(x)(2x)=2x^2ft^2
area of only walk=(2x^2+6x+4)-2x^2=2x^2+6x+4-2x^2=(6x+4)ft^2
c.area of gravel=76ft^2
area of only walk=76ft^2
6x+4=76
6x=72
x=12ft
l=2x=2*12=24ft
w=x=12ft
area of garden=24*12=288ft^2
therefore the garden should be of 288ft^2.