SOLUTION: A square pool has length p. The border of the pool is 1 ft. wide. The combined area of the border and the pool is 400ft squared. Find the area of the pool

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A square pool has length p. The border of the pool is 1 ft. wide. The combined area of the border and the pool is 400ft squared. Find the area of the pool      Log On


   

Question 31868This question is from textbook algebra
: A square pool has length p. The border of the pool is 1 ft. wide. The combined area of the border and the pool is 400ft squared. Find the area of the pool This question is from textbook algebra

Found 2 solutions by Paul, checkley71:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
you may need to draw a diagram for better understanding:

 __________________        

| 1______________1 |

|1|              |1|

| |             p| |

|1|______________|1|P+2

|_1______________1_|

Total area = 400ft.

Total length for a side = p+2:

Area of a square is given by n^2:

%28p%2B2%29%5E2=400

p%5E2%2B4%2B4p=400

p%5E2%2B4p-396=0

Factor:

(p-18)(p+22)=0

p=18 or p=-22

Remove the negative, and hence, the length for the square is 18ft long, and the area of the pool is 324ft squared.

18^2=324ft

Paul.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE TOTAL AREA OF THE POOL AND THE BORDER IS (X+2)~2=400 OR X~2+4X+4=400 OR
X~2+4X-396=0 FACTORING THIS EQUATION WE GET (X-18)(X+24) OR X=18 & X=-24
THEREFORE THE POOL IS 18 FEET LONG AND WIDE.
PROOF (18+2)~2=400 OR 20~2=400 OR 400=400