a 20 ft by 40 ft rectangle swimming pool is surrounded by a walk way of uniform width. if the total area of the walkway is 396square ft how wide is the hall way

Question

detailed description please

 

I have another problem if you don't mind

A toy rocket is launched from a 2.8m high platform in such a way that its height, h(in meters), after t seconds is given by the equation h=-4.9t^2+18.9t+2.8. how long will it take for the rocket to hit the ground?

     

Answer 1

So, the first one.

First step, sketch out the rectangle. Drawing a picture is always the best thing you can do to help your brain comprehend the problem.

      

             40

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             40

 

The important thing to note, is that the surrounding walkway is of uniform width. Sketch that.

 

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We don't know the extra bit of area that is added on the sides, or on the top. But we do know that, since the width of the sidewalk is uniform, the area added on the top, bottom, left, and right is due to the same width. Let's call this x.

 

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|         |                                                         |        |

|         |x                                                     x|        |

|_____|_________________________________|____|                                          

|    x   |                                                          |   x  |

|         |                                                          |       |

 

And you can draw the bottom in the same manner. We know that the area of the sidewalk is 396. So set an equation were 396 = the sum of the area of each piece.
396 = 4(x * x) [that's the four corner pieces] + 2 (40*x) [that's the two long rectangle pieces] + 2 (20*x) [the two narrow rectangle pieces]

thus:

396 = (4)x^2 + 120x

0 = (4)x^2 + 120x - 369

 

Use the quadratic equation to solve.