Question

determine the dimensions of the kitty pool. You will know the combined area of the pool and the pad do you have some clues about the length and the width that are related.

Answer 1

Answer: We have to find the dimension of a pool, provided the total area of it is 5000 square feet, and some clues and algebraic relation between length and width:

Diagram:

The diagram according to the information provided is as follows:

The following mathematical equation relates the total area of the pool with the dimensions of the pool:

`A=5000ft^2=2[h* l]+2[w* l]+2[w* h]\Rightarrow(1)`

Plugging in the known variables in equation (1) gives a solvable equation as follows:

`\begin{gathered} A=5,000ft^2=2[20ft*(w+30)]+2[w*(w+30)]+2[w*20ft] \\ \\ \\ 5000ft^2=2(20w+600)+2(w^2+30w)+2(20w) \\ \\ 5000ft^2=40w+1200+2w^2+60w+40w \\ \\ 2w^2+140w+1200=5000 \\ \\ 2w^2+140w+1200-5000=0 \\ \\ 2w^2+140w-3800=0\Rightarrow(2) \end{gathered}`

The solution to the quadratic equation (2) is as follows:

`\begin{gathered} 2w^2+140w-3800=0 \\ \\ \text{ Using the quadratic formula we get:} \\ \\ w=(-(140)\pm√((140)^2-(4*2*-3800)))/((2*2))=(-140\pm√(19600+30400))/(4) \\ \\ w=(-140\pm√(50000))/(4)=(-140\pm223.61)/(4) \\ \\ w=(223.61-140)/(4)=20.9025 \\ \\ w=(-140-223.61)/(4)=-90.9025 \end{gathered}`

Therefore the dimensions are:

`\begin{gathered} w=20.90ft \\ \\ l=w+30\Rightarrow l=50.90ft \\ \\ h=20ft \end{gathered}`