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...

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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embizze | High School Teacher | (Level 1) Educator Emeritus

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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`

`54+30x+4x^2=108`

`4x^2+30x-54=0`

`2x^2+15x-27=0`

`(2x-3)(x+9)=0`

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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