SOLUTION: A rectangular lawn 40 ft long and 30 ft wide has a path of uniform width around it. If the area of the path is 800 sq. ft. Find the width of the path

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Question 473367: A rectangular lawn 40 ft long and 30 ft wide has a path of uniform width around it. If the area of the path is 800 sq. ft. Find the width of the path
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular lawn 40 ft long and 30 ft wide has a path of uniform width around it.
If the area of the path is 800 sq. ft. Find the width of the path
:
Let x = the width of the path
:
The overall dimensions, including the surrounding path: (2x+40) by (2x+30)
:
Overall area - lawn area = path area
[(2x+40)*(2x+30)] - (40*30) = 800
:
FOIL & Multiply
4x^2 + 60x + 80x + 1200 - 1200 = 800
:
A quadratic equation
4x^2 + 140x - 800 = 0
;
simplify, divide by 4
x^2 + 35x - 200 = 0
:
Factors to
(x+40)(x-5) = 0
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The positive solution is what we want here
x = 5 ft is the width of the path
:
:
Check solution by finding the areas
(10+40) * (10+30) = 2000 - 1200 = 800