Question

a rectangular pool has an area of 640 square feet. the is 12 feet shorter than the width. the length of the pool is feet and the width of the pool is feet.

Answer 1

Given:

Area of rectangular pool = 640 square feet

The length is 12 feet shorter than the width.

To find:

The length and width of the pool.

Solution:

Let width of the pool = x feet

Then, Length of the pool = (x-12) feet

Area of a rectangle is

$Area=length\times width$

$Area=(x-12)\times x$

Area of pool is 640 square feet. So,

$(x-12)x=640$

$x^2-12x-640=0$

Splitting the middle term, we get

$x^2-32x+20x-640=0$

$x(x-32)+20(x-32)=0$

$(x+20)(x-32)=0$

Using zero product property, we get

$x=-20,32$

Dimensions cannot be negative. So, x=32.

Now,

Width of the pool = 32 feet

Length of the pool = 32-12 = 20 feet

Therefore, the length of the pool is 20 feet and width is 32 feet.