math word problem

Question

A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area enclosed within the perimeter of the deck is 3696 square feet. What is the width of the deck?

Answer 1

Draw a diagram of the pool and deck.

The width of the deck is x.

Notice that the deck adds x at both ends of each dimension.

The outer dimensions of the deck are 40+2x and 30+2x.

The area enclosed by the deck is thus:

(2x+40)(2x+30) = 3696.

Solve for x.

4x²+140x+1200=3696

4x²+140x-2496=0

Simplify (divide both sides by 4)

x²+35x-624=0

(x-13)(x+48)=0

x=13, -48

The negative value for x doesn't make sense.  Discard it.

x = 13 feet

 

Answer 2

(30+2x)(40+2x)-1200=3696

1200+60x+80x+4x² -1200=3696

4x² +140x-3696=0

x=17.58 or -52.58

since length is positive, the only solution is 17.58