Answer:
The dimensions of the pool are:
Width: 8.944 feet
Length: 17.888 feet
Step-by-step explanation:
From Geometry, the area of a rectangle ([tex]A[/tex]), measured in square feet, is determined by the following equations:
[tex]A = w\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width, measured in feet.
[tex]l[/tex] - Length, measured in feet.
If we know that [tex]w = x[/tex], [tex]l = 2\cdot x[/tex] and [tex]A = 160\,ft^{2}[/tex], then we get the following second order polynomial:
[tex]2\cdot x^{2}-160 = 0[/tex] (1)
And we solve the expression for [tex]x[/tex]:
[tex]2\cdot x^{2} = 160[/tex]
[tex]x^{2} = 80[/tex]
[tex]x = \sqrt{80}\,ft[/tex]
[tex]x \approx 8.944\,ft[/tex]
Then, the dimensions of the pool are, respectively:
[tex]w \approx 8.944\,ft[/tex] and [tex]l \approx 17.888\,ft[/tex]
