SOLUTION: a path of uniform surrounds a rectangular garden that is 5m wide and 12 m long the area of the path is 168m sqaured find the width of the path

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Question 1020309: a path of uniform surrounds a rectangular garden that is 5m wide and 12 m long the area of the path is 168m sqaured find the width of the path
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A path of uniform width surrounds a rectangular garden that is 5 m wide and 12 m long.
The area of the path is 168 m squared. Find the width of the path.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Your equation is 

(5+2x)*(12+2x) - 5*12 = 168,

where x is an unknown width of the path. 
The equation's left side is the difference between the areas of the larger rectangle and the area 
of smaller rectangle which represents the garden.
The right side is the given area of the surrounding path.

Simplify the equation:

 = ,   or

 = .

Use the quadratic formula to find the roots.

The only root which fits is positive x = 3.5.

Check: (5+2*3.5)*(12+2*3.5) - 60 = 12*19 - 60 = 168.   (OK!)

Answer. The width of the path is 3.5 m.


Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Draw this.
The area of the path is 168 m^2
That is 2(5+2x)*x+24x
Therefore 10x+4x^2+24x=168
4x^2+34x-168=0
2x^2+17x-84=0
(2x-7)(x+12)=0
x=3.5 m. ANSWER.
The whole area is 19*12=228 sq m.
Subtract the area of the garden, 60m, and get 168 m^2.
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