SOLUTION: A rectangular garden is two times as long as it is wide and is surrounded by a brick wall 1.5 meters wide. Find the dimensions of the garden if the area of the walk is 171 meters s

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Question 943369: A rectangular garden is two times as long as it is wide and is surrounded by a brick wall 1.5 meters wide. Find the dimensions of the garden if the area of the walk is 171 meters squared.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Which is it? Brick wall or a walk, which surrounds the garden? On ground level the area occupied around the garden has a uniform width of 1.5 meters. This can be used for the ground level area surrounding the garden.

w width of garden
L length of garden
L=2w;
u, the uniform width of the surrounding area;
u=1.5

%28w%2B2u%29%28L%2B2u%29-wL=171, account for the surrounding path or area
%28w%2B2u%29%282w%2B2u%29-w%282w%29=171
2w%5E2%2B4uw%2B2uw%2B4u%5E2-2w%5E2=171, notice inverse to 2w^2...
6uw%2B4u%5E2=171
the single variable here is just w.
6uw=171-4u%5E2
w=%28171-4u%5E2%29%2F%286u%29
substitute for u.
w=%28171-4%281.5%29%5E2%29%2F%286%2A1.5%29
w=162%2F9
highlight%28w=18%29, and according to given, highlight%28L=36%29.