Need assistance with word problem

[richpa]

Hi Everyone

I have the following basic maths/word problem.

A pool has a perimeter of 46m. It has a path built around it with a width of (x - 8)m. The paths area is 140m2.
What are the pools dimensions given the above?

Thankyou

 

[Dr.Peterson]

This looks more like an algebra problem than arithmetic.

Please show us what you have tried (as we ask you to do) so we can see where you need help, and what kind of help is appropriate. Can you work with a system of equations in two variables, or do you need to work with only one variable? If you can only do arithmetic, you'll probably need trial and error.

 

[HallsofIvy]

I suggest you first draw a picture! Call the length of the pool "a" meters and the width "b" meters. The length of the path along the 2 sides is 2a. But the length of the path along the top and bottom is 2b+ 4(x- 8) (because I did not include the four "turning the corners" in the length if the sides). The path's area is 2a(x- 8)+ (2b+ 4(x-8)(x- 8)= 140. The pools perimeter is 2a+ 2b= 46. That is only 2 equations in three unknown values (a, b, and x) but I presume you are being asked to find a and b in terms of x.

 

[Steven G]

For the OP. Professor Halls meant to write 2a(x- 8)+ (2b+ 4(x-8))(x- 8)= 140

 

[HallsofIvy]

Thanks!