SOLUTION: you are planning a rectangular garden. Its length is twice its width x. You want a walkway 2ft wide around the garden.
a. Write an expression for the area of the garden and wal
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-> SOLUTION: you are planning a rectangular garden. Its length is twice its width x. You want a walkway 2ft wide around the garden.
a. Write an expression for the area of the garden and wal
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Question 410593: you are planning a rectangular garden. Its length is twice its width x. You want a walkway 2ft 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 76ft^2 and want to use it all on the walk. How big should you make the garden? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! you are planning a rectangular garden.
Its length is twice its width x.
You want a walkway 2ft wide around the garden.
:
x = the width of the garden
then
2x = the length
and
x(2x) = 2x^2; is the area of the garden
;
a. Write an expression for the area of the garden and walk.
Area including the walk (a 2' walk all the way around, adds 4' to each dimension):
A = (2x + 4)(x + 4)
FOIL
A = 2x^2 + 8x + 4x + 16
A = 2x^2 + 12x + 16, overall area
:
B. Write an expression for the area of the walk only.
Overall area - garden area = walkway area
2x^2 + 12x + 16 - 2x^2 = Walkway area
Find the walkway area (A)
A = 2x^2 - 2x^2 + 12x + 16
A = 12x + 16, walkway area
:
c. You have enough gravel to cover 76ft^2 and want to use it all on the walk.
How big should you make the garden?
:
Replace A in the above equation with 76, find x which will give the dimension of the garden
12x + 16 = 76
12x = 76 - 16
12x = 60
x =
x = 5 ft is the width of the garden
2(5) = 10 ft is the length
:
:
See if that makes sense
(5+4)*(10+4) = 126 sq/ft overall area
Garden: 5*10 = 50 sq/ft
---------------------------
Walkway area 76 sq/ft
