SOLUTION: A square swimming pool with a side measuring 16m is to be surrounded with a uniform rubberized floor covering of width x. If the area of the floor covering equals the area of the p

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A square swimming pool with a side measuring 16m is to be surrounded with a uniform rubberized floor covering of width x. If the area of the floor covering equals the area of the p      Log On


   

Question 118718: A square swimming pool with a side measuring 16m is to be surrounded with a uniform rubberized floor covering of width x. If the area of the floor covering equals the area of the pool, find the width of the rubberized covering.
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
AREA OF POOL=16*16=256 METERS^2
AREA OF THE THE SURROUNDING FLOOR=256 METERS^2
TOTAL AREA 2*256=512 METERS^2
(16+2X)^2=512
256+64X^2+4X^2=512
4X^2+64X+256-512=0
4X^2+64X-256=0
4(X^2+16X-64)=0
USING THE QUADRATIC EQUATION WE GET:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(-16+-SQRT[16^2-4*1*-64])/2*1
X=(-16+-SQRT[256+256])/2
X=(-16+-SQT512)/2
X=(-16+-22.62)/2
X=(-16+22.62)/2
X=6.62/2
X=3.31M ANSWER FOR THE WIDTH OF THE SURROUNDING FLOOR.
PROOF
(16+2*3.31)^2=512
(16+6.62)^2=512
22.62^2=512
512=512