SOLUTION: The Length of Hillcrest Garden is 6 feet more than its width. A walkway 3 feet wide surrounds the outside of the garden. The total area of the walkway is 288 square feet. Find the

Algebra ->  College  -> Linear Algebra -> SOLUTION: The Length of Hillcrest Garden is 6 feet more than its width. A walkway 3 feet wide surrounds the outside of the garden. The total area of the walkway is 288 square feet. Find the       Log On


   

Question 346355: The Length of Hillcrest Garden is 6 feet more than its width. A walkway 3 feet wide surrounds the outside of the garden. The total area of the walkway is 288 square feet. Find the dimensions of the garden.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=W+6
(L+6)(W+6)-LW=288 REPLACE L WITH (W+6)
[(W+6)+6](W+6)]-(W+6)W=288
[(W+12)(W+6)]-(W^2+6W)=288
W^2+18W+72-W^2-6W=288
12W=288-72
12W=216
W=216/12
W=18 FT. FOR THE WIDTH OF THE GARDEN.
L=18+6=24 FT. FOR THE LENGTH OF THE GARDEN.
PROOF:
(24+6)(18+6)-24*18=288
30*24-432=288
720-432=288
288=288