SOLUTION: A rectangular garden is 5 ft longer than twice its width. It has a sidewalk 3 feet wide on two of the sides. The area of the sidewalk is 213 square feet. Find the dimensions of th

Algebra ->  Finance -> SOLUTION: A rectangular garden is 5 ft longer than twice its width. It has a sidewalk 3 feet wide on two of the sides. The area of the sidewalk is 213 square feet. Find the dimensions of th      Log On


   

Question 1055039: A rectangular garden is 5 ft longer than twice its width. It has a sidewalk 3 feet wide on two of
the sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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A rectangular garden is 5 ft longer than twice its width. It has a sidewalk 3 feet wide on two of
the highlight%28adjacent%29 sides. The area of the sidewalk is 213 square feet. Find the dimensions of the garden.
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x - 2y = 5,                 (1)
(x+3)*(y+3) - xy = 213.     (2)

Simplify (2) by opening the parentheses

(x+3)*(y+3) - xy = 213,   or

xy + 3x + 3y + 9 - xy = 213,   or

3x + 3y = 213-9,   or

3x + 3y = 204,    or   

x + y = 68.                 (3)

Now you have this system of two equations in two unknowns

 x - 2y =  5,               (1)
 x +  y = 68.               (3)

Distract the equation (1) from the equation (3). You will get

3y = 68 - 5 = 63.

From this point, please complete the solution on your own.