A Rectangular Pool Is 20 Feet Wide And 50 Feet Long. A Deck Used For Sunning Surrounds The Pool. The Deck Is The Same Width All The Way Around The Poo

A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the deck around the pool

 

Answer:

3 feet

Solution:

pool = 20 x 50 ft.

The area of a rectangle is given as lw, which is the length times the width.

area of the pool = 1000 ft²

area of deck only = 456 ft²

Were looking for the width of the deck (x), and the easiest way to do that would be to get the dimensions (length and width) of the total area.

total area = area of the pool + deck

total area = 1456 ft²

We know that the dimensions of the total area can be represented as:

l = 2x + 50

w = 2x + 20

Now, lets solve for the dimensions.

A = lw

1456 = (2x + 50)(2x + 20)

1456 = 4x² + 140x + 1000

364 = x² + 35x + 250

0 = x² + 35x - 114

Factor out the polynomial.

(x - 3)(x + 38) = 0

x = 3, -38

Since we are dealing with measurements, we cannot use negative values, therefore, x = 3.

The deck is 3 feet wide.