Question

dale has a square garden. He adds a 2-foot-wide walkway around his garden. If the total area of the walkway and garden is 196 square feet, find the dimensions of the garden

Answer 1

Let the side of the garden alone (without walkway) be x.  
Then the area of the garden alone is x^2.  
The walkway is made up as follows:

1) four rectangles of width 2 feet and length x, and 
 2) four squares, each of area 2^2 square feet.


The total walkway area is thus x^2 + 4(2^2) + 4(x*2).  

We want to find the dimensions of the garden.  To do this, we need to find the value of x.

Let's sum up the garden dimensions and the walkway dimensions:

x^2 + 4(2^2) + 4(x*2) = 196 sq ft

x^2 + 16 + 8x = 196 sq ft

x^2 + 8x - 180 = 0

(x-10(x+18) = 0

x=10 or x=-18.  We must discard x=-18, since the side length can't be negative.  We are left with x = 10 feet.

The garden dimensions are (10 feet)^2, or 100 square feet.