A rectangular pool is 20 feet wide and 50 feet long.

Question

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 walkway

Answer 1

The total area of the deck (456 sq ft) is the length x width of the deck and the pool MINUS the length x width of the pool. We are told the deck is the same width all around the pool, let's call this number y.  We can now define the length and width of the pool plus the deck as  

 

length= 50 + y

width= 20 +y

Area of the pool and the deck= (50+y)*(20+y)=1000+50y+20y+y^2= y^2 + 70y +1000

 

We also know that the length of the pool is 50 ft and the width of the pool is 20 ft

Therefore, we know the area of the pool:

Area= 50* 20 = 1000

 

 

We know the total area of the deck is the length x width of the deck and the pool MINUS the length x width of the pool:

 

456 sq ft = [y^2 + 70y + 1000] - 1000

456 = y^2 + 70y

 

Rearranging the equation, we get:

y^2 + 70y - 456= 0

(y-6)(y+76)=0

y= 6 or y=-76

 

Since we know that length cannot be a negative number, y must be 6. The walkway is therefore 6ft wide.