Question 778633
A particular rectangular swimming pool is twice as long as it is wide.
 There is a concrete walkway around the perimeter of the pool.
 The walkway is a constant 2 feet wide.
 The walkway has an area of 100 square feet.
 What are the dimensions of the pool?
:
let L = the length of the pool
let w = the width
:
A 2 ft walkway adds 4 ft to the length & width giving us the overall dimensions
Overall area - pool area = 100 sq ft, (area of the walkway)
(L+4)(w+4) - L*W = 100
L = 2w, replace L with 2w
(2w+4)(w+4) = 2w*w = 100
FOIL
2w^2 + 8w + 4w + 16 - 2w^2 = 100
the 2w^2's cancel leaving us with
12w = 100 - 16
12w = 84
w = 84/12
w = 7 ft is the width of the pool
therefore
2(7) = 14 ft is the length of the pool
:
:
See if this checks out, find the overall area and the area of the pool
18*11 = 198
14*7  = 98
---------------
diff: 100 sq/ft, the area of the walkway