A gardener has a 60 ft. piece of lumber. He wants to make a rectangular flower bed with the area of 216 sq. ft. out of that lumber. What are the dimensions of the flower bed? All 4 sides will be cut from that one piece of lumber.
2006-06-28 05:20:46 · 6 answers · asked by slobberknocker_usa 7 in Education & Reference ➔ Primary & Secondary Education
Perimeter = 60 = 2L + 2w
w = (60 - 2L)/2 = 30 - L
Area = 216 = Lw
216 = L (30-L)
216 = 30L - L^2
L^2 - 30L + 216 = 0
(L + 6) (L - 36) = 0
L = -6, 36
Length cannot be negative
Total Length = 36
each length = 36/2 = 18
60 = 2(18) + 2w
60-36 = 2w
24= 2w
w = 12
To check:
A = LW
A = (12)(18) =216
So, 12ft x 18 ft
2006-06-28 05:39:22 · answer #1 · answered by Dani 4 · 7⤊ 1⤋
The dimensions of the flower bed are 12 ft and 18 ft (12 ft of large and 18 ft of length)
2006-06-28 06:43:42 · answer #2 · answered by Hoang Cung 1 · 0⤊ 0⤋
12 x 18 ft
2006-06-28 05:33:50 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Let x and y be the length of the two sides. Then:
2x+2y=60
xy= 216
Then x=216/y and substituting in 2x+2y=60, you get:
2(216/y)+2y=60 and simplfying and rearranging you get
the quadratic equation:
y(squared) -30y +216 = 0
Solving by factoring or the quadratic formula the roots are 12 and 18.
2006-06-28 05:44:17 · answer #4 · answered by Tom E Lincoln 1 · 0⤊ 0⤋
Answer ...
Simultaneous equations ...
2 (l + w) = 60 ... ... ... l x w = 216
l + w = 30
l = 30 - w
... ... ... (30-w) x w = 216
... ... ... 30w -w2 = 216
... ... ... 0 = w2 - 30w + 216
... ... ... 0 = (w-18) (w-12)
Answers = w=12, l=18.
2006-06-28 05:45:17 · answer #5 · answered by robabard 5 · 0⤊ 0⤋
x(x + 9) = 4(x + 6) first do x cases x and x cases 9 and also you get 2x+9x=4(x + 6)then upload 11x=4(x + 6) now multyply 4 cases x and four cases 6 11x=4x+24 now subtract 4x from both section 7x=4 now divive eachb section through 7 wait no im incorrect sorry i presumed i knew the thanks to do component im sorry i already di d this in college yet i frogot.
2016-11-15 09:05:39 · answer #6 · answered by wesch 4 · 0⤊ 0⤋