math question?

Question

this question is so hard it took me forever to figure it out and i have the answer and whoever gets it right and shows me how they did it i will vote as best answer

A rectangular swimming pool is 50ft long and 25 ft wide. there is a walkway x ft wide surrounding the pool.

First you have to find the lenght and width of the pool with the walkway x ft.

Next you have to find the area of hte pool with the walkway in terms x. Explain!

ok if the total area of the pool and walkway is 2284 ft squared, what is the width of the walkway?

This is easy simple geometry right? Wrong! remember whoever gives the right answer and the best explaination gets my vote as best answer!

Answer 1

Length of walkway and pool = (50 + 2x)

Width of walkway and pool = (25 + 2x).

Area of pool and walkway = (50 + 2x)(25 + 2x)

(50 + 2x)(25 + 2x) = 2284.

Now you have to solve this equation to find x.

Hope this bit helps, Twiggy

Answer 2

Length is 50ft + 2x ft because there is a walkway on either side of the pool.
Width is 25 ft + 2x ft because there is a walkway on either end of the pool.
Area is Length x Width
Area = (25 + 2x)( 50 + 2x) multiply together using FOIL
Area = 1250 + 100x + 50x + 4x^2
Area = 1250 +150x + 4x^2 --This is the 'area in terms of 'x''.
Area = 2284
Therefore
1250 + 150x + 4x^2 = 2284
4x^2 + 150x + 1250 - 2284 = 0
4x^2 + 150x - 1034 = 0

Using 'Completing the Square' equation;_

x = -150 +/- sq rt[150^2 - 4(4)(-1034)] / 2(4)
x = -150 +/- sq rt [22500 + 16544] / 8
x = -150 +/- sqrt [39044] / 8
x = -150 +/- 197.5955 / 8
There are now two values for 'x' :- This is an impossible answer because it is negative - no such thing as a negative length.
x = -150 + 197.5955 / 8 = 5.949 ft (The width of walkway).!!!

Answer 3

since the width of the walkside is xft
therefore the both sides of the walkside will be xft+xft=2xft
then,the width of the pool and the walkside=(25+2x)ft
the length of the pool is 50ft
therefofe the area of the pool is LXB
area=50 X (25+2x)ftsquared
=1250+100x ftsquared (in terms of x)
if the area of the pool is 2284ftsquared
therfore,2284=1250+100x
2284-1250=100x
1034=100x
x=1034/100
x=10.34ft (width of the walkway)

Answer 4

L = 50 +2x , W = 25 + 2x ( this is obvious if u draw a sketch)
Total area = ( 50 + 2x) ( 25 + 2x )=2284
1250 + 150x + 4x^2 = 2284
4x^2 + 150x - 1034 = 0 , divide by 2
2x^2 + 75x - 517 = 0
use the quadratic formula, u will get
x = 5.95 ft , or x= - 43.45
the second answer is rejected ,we can not accept negative answer in this case.
sothe avswer is x = 5.95 ft

Answer 5

? ask a calculater