How do you find the perimeter in this word problem ?
The park department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width, with the same area as the flower bed. Calculate the perimeter outside of the path?
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We are given a rectangular flower bed 6mx9m, with a walk of constant width around the outside, the walkway having the same area as the flower bed. Find the perimeter.
(1) The area of the flower bed is 6x9=54 square meters; thus the area of the walkway is 54 square meters. The area of the entire assemblage is `108 m^2` .
(2) Let the width of the walkway be `x` . Then the area of the total figure is `(6+2x)(9+2x)` . (We add the width of the walkway to the top and bottom giving an increased width of 6+2x; we add the width of the walkway to the left and right sides giving an increased length of 9+2x)
(3) Then `(6+2x)(9+2x)=108`
By the zero product property, either `x=3/2` or `x=-9` . The latter makes no sense for the problem, so `x=3/2` .
(4) The dimensions of the flower bed and walkway are (6+3)(9+3)=9x12. Thus the perimeter is 2(9)+2(12)=42.
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