SOLUTION: the area of a garden is 120 sq. feet. the length of the garden is 1 foot less then twice the width. what are the dimensions of the garden?

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Question 133683This question is from textbook
: the area of a garden is 120 sq. feet. the length of the garden is 1 foot less then twice the width. what are the dimensions of the garden? This question is from textbook

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Area(A)=Length(l) times Width(w) or A=l*w
Let w=width
Then length(l)=2w-1
Now we are told that:
w*(2w-1)=120 or
2w^2-w=120 subtract 120 from each side
2w^2-w-120=120-120
2w^2-w-120=0 quadratic in standard form-solve using quadratic formula:
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
w+=+%281+%2B-+sqrt%28+1-4%2A2%2A%28-120%29+%29%29%2F%282%2A2%29+
w+=+%281+%2B-+sqrt%28+1%2B960%29%29%2F%284%29+
w+=+%281+%2B-+sqrt%28961%29%29%2F%284%29+
w+=+%281+%2B-31%29%2F%284%29+
Neglect the negative value for w. In this case, length and width are positive.
w=%281%2B31%29%2F4=8 ft --- width of garden
2w-1=2%2A8-1=15 ft ----length of garden
CK
A=l*w=15*8=120 sq ft
and 15=2*8-1
Hope this helps--ptaylor