SOLUTION: A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of t      Log On


   

Question 860081: A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A rectangular garden is 30 ft by 40 ft.
Part of the garden is removed in order to install a walkway of uniform width around it.
The area of the new garden is one-half the area of the old garden.
How wide is the walkway?
:
Find the original area of the garden
30 * 40 = 1200; new area will be half, 600 sq/ft
:
Let x = the width of the walkway, this subtracts 2x from both dimensions
:
(30-2x)(40-2x) = 600
FOIL
1200 - 60x - 80x + 4x^2 = 600
4x^2 - 140x + 1200 - 600 = 0
4x^2 - 140x + 600 = 0
simplify, divide by 4
x^2 - 35x + 150 = 0
Factors to
(x-5)(x-30) = 0
Two solutions
x = 5
x = 30
the reasonable solution
x = 5 ft is the width of the walkway