Question

harold goldstein and his wife elaine recently installed a built in rectangular swimming pool measuring 25 ft by 35 ft. they want to add a decorative tile border of uniform width around all sides of the pool. how wide can they make the tile border if they purchased enough tile to cover 396 sq feet? the max width of the border can be ? ft? HELP!! need solution, very confused :(

Answer 1

Want to work toghether to solve this?

Answer 2

yes, that would be great, im terrible with word problems . :)

Answer 3

No worries, here we go, imagine de pool, A= 25 and B=35 right?

Answer 4

right....

Answer 5

Now, around the pool they will build a frame, this frame will be constituted by 8 segments:
X= the widht we are looking for

S1= Rectangle = A*X = 35X
S2= Rectangle = A*X = 35X
S3= Rectangle = B*X = 25X
S4= Rectangle = B*X = 25X
S5= Square of \[X ^{2}\]
S6= Square of \[X ^{2}\]
S7= Square of \[X ^{2}\]
S8= Square of \[X ^{2}\]

Answer 6

The area we are looking for is the sum of this 8 segments, if we put this in the form of an equation we have:

\[A = 35X + 35X + 25 X + 25X + X ^{2}+X ^{2}+X ^{2}+X ^{2}\]

If we simplify it, we get a regular quadratic equation:

\[4X ^{2}+ 120X = 396\]

Answer 7

correct?

Answer 8

seems right to me :)

Answer 9

now, do you know how to solve a quadratic equation?

Answer 10

yes i believe so...the solution is 3ft, right?

Answer 11

yes

Answer 12

there you go

Answer 13

thanks :)

Answer 14

No problem mate