Answer:
The length of the rectangular pool is 30 feet and the width is 5 feet
Step-by-step explanation:
The question is
Find the length and the width of the rectangular pool
we know that
The volume of a rectangular prism (a rectangular-shaped lap pool) is equal to
[tex]V=LWH[/tex]
we have
[tex]V=900\ ft^3[/tex]
[tex]H=6\ ft[/tex]
[tex]L=2W+20[/tex]
substitute the given values in the formula of volume
[tex]900=(2W+20)W(6)[/tex]
solve for W
[tex]150=2W^2+20W[/tex]
[tex]2W^2+20W-150=0[/tex]
Simplify
[tex]W^2+10W-75=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
The solution is W=5 ft
Find the value of L
[tex]L=2(5)+20=30\ ft[/tex]
therefore
The length of the rectangular pool is 30 feet and the width is 5 feet
