SOLUTION: A swimming pool 6 m wide and 10 m long is to be surrounded by a cement path of uniform width. The area of the path is equal to the area of the pool. What is the width of the path?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A swimming pool 6 m wide and 10 m long is to be surrounded by a cement path of uniform width. The area of the path is equal to the area of the pool. What is the width of the path?      Log On


   



Question 518189: A swimming pool 6 m wide and 10 m long is to be surrounded by a cement path of uniform width. The area of the path is equal to the area of the pool. What is the width of the path?
Found 2 solutions by richscary, josmiceli:
Answer by richscary(3) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
the area of the pool is
+6%2A10+=+60+ m2
Let x = the width of the path
Both the length and width are increased by 2x
The area of the path + pool = +120+ m2
+%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120+
+60+%2B+20x+%2B+12x+%2B+4x%5E2+=+120+
+4x%5E2+%2B+32x+=+60+
+x%5E2+%2B+8x+=+15+
Complete the square

+%28+x+%2B+4%29%5E2+=+31+
+x+%2B+4+=+sqrt%2831%29+
+x+=+sqrt%2831%29+-+4+
+x+=+5.5678+-+4+
+x+=+1.5678+
The width of the path is 1.5678 m
check answer:
+%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120+
+%286+%2B+2%2A1.5678%29%2A%2810+%2B+2%2A1.5678%29+=+120+
+%286+%2B+3.1356%29%2A%2810+%2B+3.1356%29+=+120+
+9.1356%2A13.1356+=+120+
+120.0016+=+120+
close enough