SOLUTION: The rectangular garden in the picture measures 30feet by 50feet, and is surrounded by a path of uniform width around the four edges. The perimetre of the rectangle by the garden an

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Question 989392: The rectangular garden in the picture measures 30feet by 50feet, and is surrounded by a path of uniform width around the four edges. The perimetre of the rectangle by the garden and surrounding path is 224feet. Set up and solve an equation to find x, the width of the path.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Make your drawing to help in assigning variables and making an equation.
I am choosing x and y for dimensions, but w for the width of the surrounding path.

Dimensions of the outer path will be x+2w for length and y+2w for how wide the garden.
x for garden length, y for garden's how wide.

system%28p=224%2Cx=30%2Cy=50%2Cw=unknownOuterWidthofPathway%29

Only w is the unknown to solve.
Using formula for perimeter,
highlight_green%282%28x%2B2w%29%2B2%28y%2B2w%29=p%29
Solve this for w.

highlight%28w=%28p-%282x%2B2y%29%29%2F8%29

Notice that this is the difference of the outer and inner perimeters, and then divided by 8.