SOLUTION: please help me on a story problem: a rectangular swimming pool is surrounded by a cement walk of uniform width.let x represent this width. the pool measures 6m by 10m and the tota

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me on a story problem: a rectangular swimming pool is surrounded by a cement walk of uniform width.let x represent this width. the pool measures 6m by 10m and the tota      Log On


   

Question 119170This question is from textbook
: please help me on a story problem:
a rectangular swimming pool is surrounded by a cement walk of uniform width.let x represent this width. the pool measures 6m by 10m and the total are of the pool and walk is 96m^2. What is the width of the walk?
 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's draw a picture. We can see that the length of the large rectangle is 10%2B2x and the width of the large rectangle is 6%2B2x since we are adding 2x to both the length and the width.


From the drawing, we can see that the area of the large rectangle is A=%2810%2B2x%29%286%2B2x%29


Also, from the drawing, the area of smaller rectangle is:

A=L%2AW=10%2A6=60



Now since the area of the pool and the walkway is 96m%5E2, this means A=96 for the large rectangle.

A=%2810%2B2x%29%286%2B2x%29 Plug in A=96

96=4x%5E2%2B32x%2B60 Foil


0=4x%5E2%2B32x%2B60-96 Subtract 96 from both sides.



0=4x%5E2%2B32x-36 Combine like terms



0=4%28x%2B9%29%28x-1%29 Factor the right side


Now set each factor equal to zero:
x%2B9=0 or x-1=0

x=-9 or x=1 Now solve for x in each case


So our possible answers are
x=-9 or x=1


However, since a negative length/width doesn't make sense, our only solution is x=1


So the walkway is 1 meter