Question

A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool and is a constant 2 feet wide. The total area of the pool and sidewalk is 160 square feet. Find the dimensions of the pool

Answer 1

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 ($A$), measured in square feet, is determined by the following equations:

$A = w\cdot l$ (1)

Where:

$w$ - Width, measured in feet.

$l$ - Length, measured in feet.

If we know that $w = x$, $l = 2\cdot x$ and $A = 160\,ft^{2}$, then we get the following second order polynomial:

$2\cdot x^{2}-160 = 0$ (1)

And we solve the expression for $x$:

$2\cdot x^{2} = 160$

$x^{2} = 80$

$x = \sqrt{80}\,ft$

$x \approx 8.944\,ft$

Then, the dimensions of the pool are, respectively:

$w \approx 8.944\,ft$ and $l \approx 17.888\,ft$