Answer:
Dimensions of the pool will be 4.5 ft × 12 ft.
Step-by-step explanation:
Let the width of the pool = x ft
Then length of the pool will be = (2x + 3) ft
Now area of the rectangular pool = Length × width
54 = x(2x + 3)
54 = 2x² + 3x
2x² + 3x - 54 = 0
From quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex]
From the given equation,
a = 2, b = 3 and c = -54
x = [tex]\frac{-3\pm\sqrt{3^{2}-4(2)(-54)}}{2(2)}[/tex]
x = [tex]\frac{-3\pm\sqrt{9+432}}{4}[/tex]
x = [tex]\frac{-3\pm\sqrt{441}}{4}[/tex]
x = [tex]\frac{-3\pm21}{4}[/tex]
x = 4.5, -6
But x can't be negative, so x = 4.5
Now length of the pool = (2×4.5) + 3 = 12 ft
Width of the pool = 4.5 ft
Therefore, dimensions of the pool will be 4.5 ft × 12 ft
