SOLUTION: A rectangular garden has an area of 2w to the second plus 5w. It has a sidewalk 3 feet wide on all four sides of the garden. The area of the sidewalk is 210 feet. What is the numer

Algebra ->  Rectangles -> SOLUTION: A rectangular garden has an area of 2w to the second plus 5w. It has a sidewalk 3 feet wide on all four sides of the garden. The area of the sidewalk is 210 feet. What is the numer      Log On


   

Question 308517: A rectangular garden has an area of 2w to the second plus 5w. It has a sidewalk 3 feet wide on all four sides of the garden. The area of the sidewalk is 210 feet. What is the numeric dimensions of the garden?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular garden has an area of 2w^2 + 5w.
L = length, w = width
L = area/width
L = %282w%5E2+%2B+5w%29%2Fw
L = 2w + 5
:
It has a sidewalk 3 feet wide on all four sides of the garden.
that adds 6' to each garden dimension
Overall dimensions
L = 2w + 5 + 6
L = 2w + 11
w = w + 6
Overall area;
(2w+11)*(w+6) = 2w^2 + 12w + 11w + 66
2w^2 + 23w + 66; overall area
:
The area of the sidewalk is 210 feet.
Overall area - garden area = 210
(2w^2 + 23w + 66) - (2w^2 + 5w) = 210
Remove brackets combine like terms:
2w^2 - 2w^2 + 23w - 5w = 210 - 66
18w = 144
w = 144%2F18
w = 8
:
What is the numeric dimensions of the garden?
w = 8 ft is the width
and
L = 2(w) + 5
L = 2(8) + 5
L = 16 + 5
L = 21 ft is the length
:
:
:
Check solution
(27*14) - (21*8) = 210