Question

Courtney is building a rectangular wading pool.

Answer 1

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 = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

From the given equation,

a = 2, b = 3 and c = -54

x = $\frac{-3\pm\sqrt{3^{2}-4(2)(-54)}}{2(2)}$

x = $\frac{-3\pm\sqrt{9+432}}{4}$

x = $\frac{-3\pm\sqrt{441}}{4}$

x = $\frac{-3\pm21}{4}$

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

Answer 2

Answer:

width = 4.5

Length = 12

Step-by-step explanation:

Let w = width

The length is 3 ft longer than 2 times the width

L =2 w+3

The Area is

A = l*w

54 = (2w+3) (w)

Distribute

54 = 2w^2 +3w

Subtract 54 from each side

54-54 = 2w^2 +3w - 54

0 = 2w^2 +3w - 54

Factor

0=(2w-9)(w+6)

Using the zero product property

0 = 2w-9    0 = w+6

2w=9       w=-6

w = 9/2   w = -6

Since we cannot have negative dimensions

w = 9/2

l = 2(9/2) +3  = 9+3  =12