SOLUTION: The original problem was Alice is planning a rectangular garden. Its length is 3 ft less than twice its width. Its area is 170 ft ^2. Find the dimensions of the garden. We must

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: The original problem was Alice is planning a rectangular garden. Its length is 3 ft less than twice its width. Its area is 170 ft ^2. Find the dimensions of the garden. We must      Log On

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Question 35455This question is from textbook prentic hall mathematics algebra 1
: The original problem was Alice is planning a rectangular garden. Its length is 3 ft less than twice its width. Its area is 170 ft ^2. Find the dimensions of the garden. We must write an equation and solve it. I already made the equation, which is (2w-3)(w)=170, but I do not know how to solve it. Could you show it step-by-step?This question is from textbook prentic hall mathematics algebra 1

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width of the rectangle
2w -3 = length of the rectangle
The equation is
LW+=+A
w+%282w-3%29+=+170
2w%5E2+-+3w+-170+=+0
This equation probably factors. By trial and error (or by using the quadratic formula if you are not good at factoring!!)
%282w+%2B+17%29%28w-10%29+=+0
w=-17%2F2 or w=10

Reject the negative answer since a width of a rectangle cannot be negative.
w= 10 feet
L = 2w-3 = 17 feet
Final answer is 10 feet by 17 feet.

Check the answer since 10x17 = 170 square feet.

R^2 at SCC